THE  BUILDING  TRADES 
POCKETBOOK 


A  HANDY  MANUAL 
OF  REFERENCE  ON 


BUILDING  CONSTRUCTION 

INCLUDING 

Structural  Design,  Masonry,  Bricklaying,  Carpentry, 
Joinery,  Roofing,  Plastering,  Painting, 
Plumbing,  Lighting,  Heating, 
and  Ventilation 


BY 

The  International  Correspondence  Schools 

SCRANTON,  PA. 


1st  Edition ,  70th  Thousand,  7th  Impression 


Scranton,  Pa. 

THE  COLLIERY  ENGINEER  CO. 


7  H 

j  *■  .  / 

T<r  7; 

/  n  r/  ^ 


Copyright,  1899,  by 

THE  COLLIERY  ENGINEER  CO. 

H/Z  rights  reserved. 


K 


PRINTED  BY 

International  Textbook  Company, 

Scranton,  Pa. 

7889 


PREFACE* 


This  Pocketbook  is  intended  for  the  use  of  all 
persons  connected  with  The  Building  Trades,  and 
contains  many  features  not  found  in  similar 
publications.  In  addition  to  tables  giving  the 
properties  of  materials  used  in  construction, 
practical  rules  for  laying  out  work,  and  data  valu¬ 
able  for  reference,  it  presents  approved  methods 
for  solving  the  problems  involving  strength  and 
stability,  which  occur  in  building  practice.  The 
processes  of  calculation  are  clear  and  intelligible, 
and  those  who  are  acquainted  with  simple  arith¬ 
metic  will  have  no  difficulty  in  following  them. 

Among  the  subjects  considered  are  the  loads 
on  structures  ;  the  strength  of  materials  ;  the  bear¬ 
ing  capacity  of  soils ;  the  width  and  thickness  of 
footing  courses ;  the  dimensions  of  piers  and  their 
foundations;  the  thickness  of  walls  for  different 
classes  of  buildings;  and  the  various  kinds  of 
stone  and  brick  masonry.  Careful  analyses  are 
made  of  columns,  beams,  and  arches  of  iron, 
steel,  wood,  and  stone,  and  of  the  design  and 


IV 


PREFACE. 


construction  of  roof  trusses  in  wood  and  steel. 

'  Tlie  features  of  detail  peculiar  to  structural  work 
are  also  fully  explained  and  illustrated. 

Constructive  details  pertaining  to  Masonry, 
Bricklaying,  Plastering,  Carpentry,  Joinery, 
Stairbuilding,  Roofing,  and  Painting  are  treated 
comprehensively,  and  much  new  information  is 
given  on  the  Computation  of  Quantities  and  the 
Costs  of  Materials. 

There  is  no  other  pocketbook  published  which 
fully  treats  of  American  Plumbing,  Gas-fitting, 
Heating,  and  Ventilation.  The  chapters  on  these 
subjects  contain  tables,  rules,  formulas,  recog¬ 
nized  maxims,  hints  on  the  best  modern  practice 
and  on  the  most  approved  apparatus  and  materi¬ 
als,  with  numerous  sketches  and  practical  infor¬ 
mation  never  before  published. 

The  demand  for  a  handy,  serviceable  volume 
devoted  entirely  to  the  building  interests,  has 
induced  the  production  of  “  The  Building  Trades 
Pocketbook,”  and  it  will  be  found  to  be  a  valuable 
aid  to  Architects,  Engineers,  Contractors,  Build¬ 
ers,  and  Artisans. 

The  International  Correspondence  Schools, 

January  2,  1899.  Scranton,  Pa. 


THE 


BUILDING  TRADES 

POCKETBOOK. 


ARITHMETIC. 


SIGNS  USED  IN  CALCULATION. 


+  Plus,  indicates  addition  ;  thus,  10  +  5  is  15. 

—  Minus,  indicates  subtraction ;  thus,  10  —  5  is  5. 

X  Multiplied  by  indicates  multiplication;  thus,  10  X  5  is  50. 
-r-  Divided  by,  indicates  division;  thus,  10  -h  5  is  2. 

=  Equal  to,  indicates  equality;  thus,  12  in.  =  1  ft. 


called  parenthesis,  bracket,  and  brace, 


respectively,  have  the  same  meaning,  and  signify  that  the 
operations  indicated  within  them  are  to  he  performed  first; 
or,  if  more  than  one  is  used,  that  indicated  in  the  inner  one  is 
to  be  effected  first.  Thus,  in  the  expression  5(7  —  2),  the 
subtraction  is  to  be  made  before  multiplying  by  5.  Again,  in 


within  the  parenthesis  is  made  first ;  the  remainder  is  added 
to  a,  and  one-half  the  sum  found. 

- ,  called  the  vinculum,  is  used  for  the  same  purpose  as 

the  parenthesis,  but  chiefly  in  connection  with  the  sign 


j/ ;  thus,  j/ 


.  ,  called  the  decimal  point,  is  placed  in  a  number  con¬ 
taining  decimals,  to  fix  the  value  of  the  number;  thus,  12.5 
is  12  and  T6ff ;  1.25  is  1  and  ^5<j  ;  etc. 

S2  means  that  the  number  8  is  to  be  squared ;  thus,  82  =  8 
X  8  =  64. 


1 


2 


ARITHMETIC. 


83  means  that  the  number  8  is  to  be  cubed;  thus,  83  =  8  X  8 
X  8  =  512. 

\/  ,  called  the  radical  sign,  means  that  some  root  of  the 

expression  under  it  is  to  he  found ;  if  used  \without  a  small 

index  figure,  it  means  square  root ;  thus,  j/  64  =  8. 

y7  mean  that  the  cube  or  the  fourth  root  is  to  be 

€ound,  the  index  figure  indicating  the  root ;  thus,  f/ 27  —  3. 

:  :  :  :  means  proportion ;  thus,  3:4  :  :  6  :  8  is  read  Sis  to  4 
as  6  is  to  8.  Instead  of  the  :  :  sign,  the  equality  sign  =  is 
often  substituted  ;  thus,  3:4  =  6:8. 

°  '  "  mean  degrees,  minutes,  and  seconds;  as,  60°  15'  15", 
which  is  read  60  degrees,  15  minutes,  15  seconds. 

'  "  also  mean  feet  and  inches ;  thus,  7'  6"  is  read  7  feet 
6  inches. 

(read  pi)  means  the  ratio  of  the  circumference  of  a 


1 T 


circle  to  the  diameter  and  =  3.1416. 

2  (read  sigma )  means  summation;  thus,  2(<z  +  6)  means 
that  there  are  several  values  for  both  a  and  b,  and  that  the 
sum  of  all  is  to  be  found. 


FRACTIONS. 

It  is  taken  for  granted  that  the  reader  knows  how  to  per¬ 
form  the  common  operations  of  addition,  subtraction,  etc., 
where  only  whole  numbers  are  used  ;  but,  when  there  are 
mixed  or  fractional  numbers,  a  little  refreshment  of  the 
memory  may  be  desirable  to  some ;  hence,  a  little  space  is 
devoted  to  this  elementary  branch  of  arithmetic. 


COMMON  FRACTIONS. 

The  numerator  of  a  fraction  is  the  number  above  the  bar ; 
and  the  denominator  is  the  number  beneath  it ;  thus,  in  the 
fraction  $,  3  is  the  numerator  and  4  is  the  denominator.  Two 
or  more  fractions  having  the  same  denominator  are  said  to 
have  a  common  denominator.  By  “reducing  fractions  to  a 
common  denominator  ”  is  meant  finding  such  a  denominator 
as  will  contain  each  of  the  given  denominators  without  a 


FRACTIONS. 


3 


remainder,  and  multiplying  each  numerator  by  the  number 
of  times  its  denominator  is  contained  in  the  common 
denominator.  Thus,  the  fractions  £,  f ,  and  TB  have,  as  a  com¬ 
mon  denominator,  16 ;  then,  i  —  fs  ;  £  =  is ;  re  —  ts* 

By  “reducing  a  fraction  to  its  lowest  terms”  is  meant 
dividing  both  numerator  and  denominator  by  the  greatest 
number  that  each  will  contain  without  a  remainder;  for 
example,  in  ,  the  greatest  number  that  will  thus  divide  14 

14  —  2 

and  16  is  2 ;  so  that,  ■  ’  ,  =  f ,  which  is  reduced  to  the 

lb  -5-  2 

lowest  terms. 

A  mixed  number  is  one  consisting  of  a  whole  number  and 
a  fraction,  as  7f. 

An  improper  fraction  is  one  in  which  the  numerator  is 
equal  to,  or  greater  than,  the  denominator,  as  Y*  This  is 
reduced  to  a  mixed  number  .by  dividing  17  by  8,  giving  2£.  If 
the  numerator  is  less  than  the  denominator,  the  fraction  is 
termed  proper.  A  mixed  number  is  reduced  to  a  fraction  by 
multiplying  the  whole  number  by  the  denominator,  adding 
the  numerator,  and  placing  the  sum  over  the  denominator ; 


(1X8)  +7 
8 


15 

8' 


thus,  1^-  = 

O 


To  add  fractions  or  mixed  numbers.  If  fractions  only, 
reduce  them  to  a  common  denominator,  add  partial  results, 
and  reduce  sum  to  a  whole  or  mixed  number.  If  mixed 
numbers  are  to  be  added,  add  the  sum  of  the  fractions  to  that 
of  the  whole  numbers ;  thus,  1\  +  2i  =  (1  +  2)  +  (f  +  |)  =  4£. 

To  subtract  two  fractions  or  mixed  numbers.  If  ' they  are 
fractions  only,  reduce  them  to  a  common  denominator,  take 

14  _  9 

less  from  greater,  and  reduce  result ;  as,  l  in.  —  -A  in.  =  —— — 

lb 

=  in.  If  they  are  mixed  numbers,  subtract  fractions  and 
whole  numbers  separately,  placing  remainders  beside  one 
another;  thus,  3£  in.  —  2\  in.  =  (3  —  2)  +  (I  —  |)  =  If  in. 
With  fractions  like  the  following,  proceed  as  indicated ; 


1|  in.;  7  in.  —  4£  in.  =  (6  +  |)  —  4f  =  2}  in. 

To  multiply  fractions.  Multiply  the  numerators  together, 
and  likewise  the  denominators,  and  divide  the  former  by  the 


4 


ARITHMETIC. 


.  ..  1.  .  .  3  .  5  .  1X3X5  15  , 

latter ;  thus,  -  in.  X  ^  in.  Xg  m.  =  2X4X8  =  64  CU' ln>  If 

mixed  numbers  are  to  be  multiplied,  reduce  them  to  frac* 
tions,  and  proceed  as  above  shown ;  thus,  1£  in.  X  3£  in.  — 
f  X  =  -3g-  =  4|  sq.  in. 

To  divide  fractions.  Invert  the  divisor  (i.  e.,  exchange 
places  of  numerator  and  denominator)  and  multiply  the 
dividend  by  it,  reducing  the  result,  if  necessary ;  thus, 
|  -r-  f  |  X  I  =  IS  =  5  =  li-  If  there  are  mixed  numbers, 
reduce  them  to  fractions,  and  then  divide  as  just  shown ; 
thus,  If  3*  =  ¥  y,  or  J#  X  A  =  -Nt  =  i- 


DECIMAL  FRACTIONS. 

In  decimals,  whole  numbers  are  divided  into  tenths,  hun* 
dredths,  etc.;  thus,  A  Is  written  .1 ;  .08  is  read  Tfc,  the  value  of 
the  number  being  indicated  by  the  position  of  the  decimal 
point ;  that  is,  one  figure  after  the  decimal  point  is  read  as 
so  many  tenths ;  two  figures  as  so  many  hundredths ;  etc. 
Moving  the  decimal  point  to  the  right  multiplies  the  number 
by  10  for  every  place  the  point  is  moved ;  moving  it  to  the 
left  divides  the  number  by  10  for  every  place  the  point  is 
moved.  Thus,  in  125.78  (read  125  and  As)>  if  the  decimal 
point  is  moved  one  place  to  the  right,  the  result  is  1,257.8, 
which  is  10  times  the  first  number ;  or,  if  the  point  is  moved  to 
the  left  one  place,  the  result  is  12.578  which  is  A  the  first  num¬ 
ber,  moving  the  point  being  equivalent  to  dividing  125.78  by  10. 

Annexing  a  cipher  to  the  right  of  a  decimal  does  not 
change  its  value ;  but  each  cipher  inserted  between  the  deci¬ 
mal  point  and  the  decimal  divides  the  decimal  by  10 ;  thus,  in 


125.078,  the  decimal  part  is  A  °f  -78.  201  257 

To  add  decimals.  Place  the  numbers  so  that  12.965 

the  decimal  points  are  in  a  vertical  line,  and  43.005 

add  in  the  ordinary  way,  placing  the  decimal  920.600 
point  of  the  sum  under  the  other  points.  1,077.827 

To  subtract  decimals.  Place  the  number  to 
be  subtracted  with  its  decimal  point  under  917.678 
that  of  the  other  number,  and  subtract  in  the  482.710 

ordinary  way.  434.968 


FRACTIONS. 


5 


To  multiply  decimals.  Multiply  in  the  ordinary  way,  and 
point  off  from  the  right  of  the  result  as  many  figures  as  there 
are  figures  to  the  right  of  the  decimal  points  in 
both  numbers  multiplied ;  thus,  in  the  example 
here  given,  there  are  three  figures  to  the  right 
of  the  points,  and  that  many  are  pointed  off  in 
the  result.  If  either  number  contains  no  deci¬ 
mal,  point  off  as  many  places  as  are  in  the 
number  that  does. 

If  a  result  has  not  as  many  figures  as  the  sum  of  the  deci-  _ 
mal  places  in  the  numbers  multiplied,  prefix  enough  ciphers 
before  the  figures  to  make  up  the  required  number  of  places, 
and  place  the  decimal  point  before  the  ciphers.  Thus,  in  .002 
X  .002,  the  product  of  2  X  2  =  4 ;  but  there  are  three  places  in 
each  number ;  hence,  the  product  must  have  six  places,  and 
five  ciphers  must  be  prefixed  to  the  4,  which  gives  .000004. 

To  divide  decimals.  Divide  in  the  usual  way.  If  the  divi¬ 
dend  has  more  decimal  places  than  the  divisor,  point  off,  from 
the  right  of  the  quotient,  the  number  of  places  in  excess.  If 
it  has  less  than  the  divisor,  annex  as  many  ciphers  to  the 
decimal  as  are  necessary  to  give  the  dividend  as  many  places 
as  there  are  in  the  divisor;  the  quotient  will  then  have 


21.72 

34.1 

2172 

8688 

6516 

740.652 


no  decimal  places. 


=  3. 


For  example, 


2.5 


10.3; 


82.5 


2.75 


82.50 

2.75 


To  carry  a  division  to  any  number  of  decimal  places. 
Annex  ciphers  to  the  dividend,  and  divide,  until  the  desired 
number  of  figures  in  the  quotient  is  reached,  which  are 
pointed  off  as  above  shown.  Thus,  36.5  -v-  18.1  to  three  decimal 

places  =  =  2.016+.  (The  sign  +  thus  placed  after  a 

lo.l 

number  indicates  that  the  exact  result  would  be  more  than 
the  one  given  if  the  division  were  carried  further.) 

To  reduce  a  decimal  to  a  common  fraction.  Place  the 
decimal  as  the  numerator ;  and  for  the  denominator  put  1 
with  as  many  ciphers  as  there  are  figures  to  the  right  of  the 
decimal  point;  thus,  .375  has  three  figures  to  the  right  of 
the  point ;  hence,  .375  in.  =  =  f  in. 


6 


ARITHMETIC. 


To  reduce  a  common  fraction  to  a  decimal.  Divide  the 
numerator  by  the  denominator,  and  point  off  as  many  places 
as  there  have  been  ciphers  annexed  ;  thus,  X3S  in.  =  3.0000  -5-  16 
—  .1875  in. 


DUODECIMALS, 


The  duodecimal  system  of  numerals  is  that  in  which  the 
base  is  12,  instead  of  10,  as  in  the  common  decimal  system. 
As  a  method  of  calculation  it  has  fallen  into  almost  entire 
disuse,  and  it  is  only  in  calculation  of  areas  that  duodecimals 
are  now  used.  When  the  work  becomes  familiar,  the  work  is 
practically  as  rapid  as  by  using  feet  and  decimals,  and  has  the 
advantage  of  being  absolutely  accurate,  which  the  decimal 
system  is  not,  as  inches  cannot  be  expressed  exactly  in  deci¬ 
mals  of  a  foot.  The  principles  upon  which  the  work  is  based 
are  as  follows :  When  feet  are  multiplied  by  feet,  or  inches 
by  inches,  the  product  is,  of  course,  square  feet  or  square 
inches,  respectively ;  but,  when  feet  are  multiplied  by  inches, 
or  vice  versa,  the  results  may,  for  want  of  a  better  name,  be 
termed  parts  (although  this  name  was  given  originally  to  the 
144th  part  of  a  square  foot).  Suppose  a  square  foot  to  be 
divided  into  144  sq.  in.;  then  a  strip  12  in.,  or  1  ft.,  long,  and 

1  in.  wide  will  correspond  to  1  part.  A  strip  5  ft.  long  and 
7  in.  wide  will  contain  7  X  5,  or  35  parts,  which,  divided  by  12 
(parts  to  a  square  foot),  equals  2  sq.ft,  and  11  parts,  or 

2  sq.  ft.  +  (11  X  12)  sq.  in.  Square  inches  may  be  reduced 
to  parts  by  dividing  by  12 ;  thus,  54  sq.  in.  =  4  parts  6  sq.  in. 
To  illustrate  these  principles,  let  it  be  required  to  find  the 
area  of  a  room  18  ft.  10  in.  long,  and  16  ft.  7  in.  wide.  Place 
feet  under  feet,  and  inches  under  inches,  thus : 


Feet. 


Inches. 

10 

_7 

4 

11 


18 

JL6 

301 

10 


10 


312  sq.  ft.  3  parts  10  sq.  in., 
312  sq.  ft.  46  sq.  in. 


or, 


INVOLUTION. 


.  7 

Begin  by  multiplying  10  in.  by  16  ft.,  which  equals  160  parts, 
or  13  sq.  ft.  4  parts.  Place  the  4  parts  in  the  inches  column,  and 
carry  the  13  sq.  ft.  Then  18  ft.  X  16  ft.  =  288  sq.  ft.  +  13  sq.  ft. 
=  301  sq.ft.  Next,  multiply  10  in.  by  7  in.  =  70  sq.  in.,  or  5 
parts  10  sq.  in.  Set  the  10  sq.  in.  to  the  right  of  the  column  ot 
parts,  as  shown.  Then,  18  ft.  X  7  in.  =  126  parts  +  5  parts  car¬ 
ried  =  131  parts ;  dividing  by  12,  131  parts  =  10  sq.  ft.  11 
parts.  Set  these  down  in  the  proper  columns  and  add,  begin¬ 
ning  at  the  right ;  4  parts  -f  11  parts  =  1  sq.  ft.  3  parts. 
Expressed  in  square  feet  and  square  inches,  the  result  is  312 
sq.  ft.  46  sq.  in.,  which  can  be  verified  by  reducing  the  given 
numbers  to  inches,  multiplying  them,  and  dividing  by  144. 


INVOLUTION. 

Involution  is  the  process  of  multiplying  a  number  by 
itself  one  or  more  times,  the  product  obtained  being  called  a 
certain  power  of  the  number.  If  the  number  is  multiplied  by 
itself,  the  result  is  called  the  square  of  the  number ;  thus,  9  is 
the  square  of  3,  since  3X3  =  9.  If  the  square  of  a  number  is 
multiplied  by  the  number,  the  result  is  called  the  cube  of  the 
number  ;  thus,  27  is  the  cube  of  3,  since  3X3X3  =  27.  The 
power  to  which  a  number  is  to  be  raised  is  indicated  by  a 
small  figure,  called  an  exponent,  placed  to  the  right  and  a  lit¬ 
tle  above  the  number  ;  thus,  72  means  that  7  is  to  be  squared  ; 
27'!  means  that  27  is  to  be  cubed,  etc. 

The  operations  of  involution  present  no  difficulty,  as 
nothing  but  multiplication  is  involved,  the  number  of  times 
the  number  is  to  be  taken  as  a  factor  being  shown  by  the 
exponent. 

If  the  number  is  a  fraction,  raise  both  numerator  and 
denominator  to  the  power  indicated. 

A  valuable  little  rule  to  memorize  for  finding  the  square  of 
a  mixed  number  in  which  the  fraction  is  £,  as  3£,  10£,  etc.,  is 
as  follows :  Multiply  the  next  less  whole  number  by  the  next 
greater,  and  add  For  example,  the  square  of  6i  is  6  (the 
next  less  number)  X  7  (the  next  greater)  +  |  =  42£;  (19i)2 
=  19  X  20  +  i  =  380i  ;  (8i)?  =  8  X  9  +  i  =  72£ ;  etc. 


8 


ARITHMETIC . 


EVOLUTION. 

Evolution  is  the  reverse  of  involution  and  is  the  process 
of  finding  one  of  the  equal  factors  of  a  number,  termed  a 
root,  which,  multiplied  by  itself  a  certain  number  of  times, 
will  give  a  product  equal  to  the  given  number.  When  the 
number  is  to  be  resolved  into  two  equal  factors,  either  on  is 
called  the  square  root ;  when  there  are  to  be  three  equal  fac¬ 
tors,  each  one  is  called  the  cube  root ;  etc.  The  operate  ns 
to  be  performed  are  indicated  by  the  radical  sign  y  and  vin 
culum  ,  and  by  an  index  figure  ;  for  square  root,  the  index 

is  omitted.  For  example,  i/64  is  read  the  square  root  of  64 

which  is  8,  since  8X8  =  64 ;  y 64  means  cube  root  of  64, 
which  is  4,  as  4  X  4  X  4  =  64. 

A  number  is  said  to  be  a  perfect  square,  or  a  perfect  cube,  etc. 
when  the  root  consists  only  of  a  whole  number  ;  thus,  64  is  a 
perfect  cube,  since  the  cube  root  is  4,  without  any  decimal. 


SQUARE  ROOT. 


In  extracting  the  square  root  of  a  number,  the  first  step  is 
to  find  how  many  figures  there  are  in  the  root.  This  is  done 
by  pointing  off  periods  of  two  figures  each,  beginning  with  the 
unit  figure ;  or,  if  the  number  is  partly  decimal,  begin  at  the 
decimal  point,  and  point  off  each  way.  Thus,  in  the  square 
root  of  625  there  are  two  figures  (6' 25) ;  in  105.0625,  there  are 
four  figures  (1'05'.06'25)  in  the  root. 

To  extract  the  square  root,  having  pointed  off  the  number 
into  periods,  proceed  as  follows  :  Let  it  be  required  to  find 
the  square  root  of  217.  There  are  two  figures  in  the  whole- 
number  part  of  the  root ;  thus,  2'17.  Find  the  number 
whose  square  is  nearest  in  value  to  the  first  period ;  in  this 
case  it  is  1.  Divide  the  first  period  (or  trial  dividend)  by 
twice  this  number  (which  call  the  trial  root),  and  to  the  quo¬ 


tient  add  ,j  the  same  number ;  thus, 


2 

1X2 


=  1.5. 


Disre¬ 


garding  the  decimal  point,  and  retaining  two  figures  of  the 
first  trial  root,  the  new  trial  root  is  15.  Add  the  second  period 
of  the  number  to  the  first  trial  dividend,  and  then  repeat  the 


E  VOL  UTION. 


9 


operations  shown ;  thus,  +  —  =  7.23  +  7.5  =  14.73,  or 

10  /\  2  2 

the  correct  root  to  two  decimal  places.  If  it  is  desired  to 
carry  the  work  further,  the  same  operations  would  be  gone 
through ;  the  next  trial  root  would  be  147  (retaining  three 
figures,  and  increasing  the  last  by  1  if  the  fourth  figure  is  5  or 


over),  disregarding  the  decimal  point;  thus, 


2' 17' 00  147 
147X2+  2 


=  73.809  +  73.50  =  147.309.  The  position  of  the  decimal  point 
is  found  by  knowing  that  there  are  two  figures  in  the  whole- 
number  or  integral  part  of  the  root,  or  the  root  is  14.7309, 
correct  to  four  decimal  places.  For  the  next  trial  root,  four 
figures  (as  1,473)  would  be  retained,  and  another  period  would 
be  annexed  to  the  trial  dividend,  etc. 

The  process  may  be  remembered  by  help  of  this  simple 
formula, 

T>  ,  D  R 
R00t  =  2R  +  2’ 


in  which  D  is  the  trial  dividend  and  R  the  trial  root.  (The 
method  of  using  formulas  is  explained  in  a  succeeding 
article.) 

If  the  first  period  is  a  perfect  square,  as  1,  4,  etc.,  use  the 
first  two  periods  as  a  trial  dividend,  add  a  cipher  to  the  trial 
root,  and  proceed  as  before  shown.  If  the  number  contains 
a  decimal,  pay  no  attention  to  the  point  till  necessary  to 
point  off  the  result. 

The  following  example  illustrates  the  last  named  princi¬ 
ples  :  What  is  the  square  root  of  427.75  ?  There  are  two  figures 
in  the  integral  part  of  the  root ;  thus,  4'27.  Since  4  is  the 
square  of  2,  4'27  is  used  as  the  first  trial  dividend,  and  20  as 

4/97  20 

the  trial  divisor ;  then  ~  ■  +  —  =  10.67  +  10  ==  20.7.  Next, 

ZU  y\  2  2 

4' 27' 75  207 

disregarding  the  decimal  poin ^  -  -f  — -  =  103.3  +  103.5 

=  206.8.  Pointing  off  the  two  figures  in  the  integral  part  01 
the  root,  the  root  is  20.68,  to  two  decimal  places. 

If  a  number  is  wholly  decimal,  the  root  will  also  be  wholly 
decimal.  If  there  arc  ciphers  immediately  following  the 
decimal  point  in  the  number,  divide  the  number  of  ciphers 


10 


ARITHMETIC. 


by  2,  and,  disregarding  any  remainder  ,'  the  result  will  be  tho 
number  of  ciphers  between  the  decimal  point  and  the  first 
significant  figure ;  thus,  in  the  root  of  .00049,  there  will  be  3 
ciphers  2  =  1  cipher  in  the  root,  which  is  .022+.  If  there 
is  no,  or  but  one,  cipher  between  the  point  and  the  first 
significant  figure  of  the  number,  there  will  be  none  immedi¬ 
ately  after  the  decimal  point  in  the  root.  The  roots  of  num¬ 
bers  having  ciphers  immediately  after  the  decimal  point 
are  found  in  the  usual  way,  disregarding  the  ciphers  (after 
pointing  off  the  periods)  until  the  position  of  the  decimal 
point  is  to  be  found. 

If  any  decimal  period  consists  of  but  one  figure,  annex  a 
cipher  to  it.  Thus,  j/.5  =  j/.50  =  .7071;  ■j/,00'00'9  = 

j/'OO'OO^JO  =  .0094+. 

If  a  number  is  a  perfect  square,  it  will  be  known  by  a 
result  being  obtained  which  is  the  same  as  the  trial  root  used 

as  divisor ;  thus,  in  y 40/96,  it  will  be  found  that  the  third 
trial  root  is  64,  and  the  quotient  obtained  is  also  64,  which  is, 

therefore,  i//4,096. 

The  square  root  of  a  fraction  is  found  by  finding  the  square 
roots  of  the  numerator  and  the  denominator,  and  dividing 
the  former  square  root  by  the  latter ;  thus, 


\4  t/ 


1  1 


l/  4  ^ 


Otherwise,  the  fraction  may  be  reduced  to  a  decimal,  and 
the  square  root  of  this  found. 


CUBE  ROOT 


The  first  step  in  extracting  cube  root  is  to  point  off  the 
number  into  periods  of  three  figures  each,  beginning  At 
the  right,  for  whole  numbers;  begin  at  the  decimal  point 
if  the  number  is  partly  decimal ;  and,  if  the  number  is 
wholly  decimal,  point  off  towards  the  right  from  the  decimal 
point.  The  cube  root  of  a  whole  number  will  contain  as 
many  figures  as  there  are  periods  and  parts  of  periods  in  the 
number.  If  the  number  is  wholly  decimal,  and  has  less  than 


EVOLUTION. 


11 


three  ciphers  between  the  decimal  point  and  the  first  signifi¬ 
cant  figure,  there  will  be  no  cipher  immediately  after  the 

decimal  point  in  the  root ;  thus,  1^.125  =  .5;  i^.OOS  =  .2.  If 
there  are  ciphers  immediately  following  the  decimal  point  in 
a  wholly  decimal  number,  the  number  of  ciphers  in  the  root 
will  be  found  by  dividing  the  number  of  ciphers  in  the  num¬ 
ber  by  3,  neglecting  any  remainder;  thus,  in  ;:l  .000008  there  are 
§  =  1  cipher,  and  the  root  is  .02.  If  the  last  period  of  a 
decimal  number  has  less  than  three  figures,  annex  enough 

figures  to  make  a  full  period ;  thus,  j^.3  —  f^.300. 

The  method  of  extracting  cube  root  is  quite  similar  to  that 
followed  for  square  root,  and  may  be  expressed  by  the  formula: 

^  ,  D  , 2R 

R°0t  3  IP  +  3  ’ 


in  which  D  is  the  trial  dividend  and  R  the  trial  root. 

The  following  example  shows  the  process  in  detail :  What 
is  the  cube  root  of  20'796.875?  Pointing  off  from  the  decimal 
point  to  the  left,  it  is  seen  that  there  are  two  figures  in  the 
whole-number  part  of  the  root.  The  number  whose  cube  is 
nearest  20  is  3 ;  then  applying  the  formula,  since  D  —  20,  and 
R  =  3,  the  next  trial  root  is 


20  2X3 

3  X  32  +  3 


.74  +  2  =  2.74. 


Retain  two  figures,  increasing  the  second  if  the  third  is  5 
or  over ;  then  the  second  trial  root  is  27.  Annexing  another 
period  to  the  trial  dividend,  and  repeating  the  above  process : 


20'796  2X27 

3  X  272  +  3 


=  9.51  +  18  =  27.51. 


For  the  third  trial  root,  retain  three  figures,  and  as  before 
neglect  the  decimal  point.  Annex  the  next  period  for  the 
new  trial  dividend,  and  repeat  the  process ;  thus, 


20'796'875  2X275 

3X2752  +  3 


91.G7  +  183.33  =  275.00 ; 


or,  pointing  off  as  above  shown,  the  root  is  27.5.  If  the  opera¬ 
tion  is  repeated  one  step  further,  a  root  is  obtained  which  is 
the  same  as  the  trial  root  used,  which  result  shows  that  the 
given  number  is  a  perfect  cube. 

If  the  first  period  is  a  perfect  cube,  use  two  periods  as  the 


12' 


ARITHMETIC. 


trial  dividend,  and  annex  a  cipher  to  the  number  whose  cu 
is  equal  to  the  first  period  ;  this  number  will  then  be  the  fi 


trial  root.  Thus,  in  y  1'728,  the  trial  root  will  be  10,  the  fi 
approximation  giving 


1'72S 


+ 


2  X  10 


=  5.76  +  6.67  =  12.43; 


3  X  102  '  3 

and  the  operations  being  continued  will  give  12  as  the  exs 
root. 

The  cube  root  of  a  fraction  may  be  found  by  extracth 
the  cube  root  of  the  numerator  and  that  of  the  denon 
nator,  and  dividing  the  former  result  by  the  latter;  thus, 

3  f27  _  #"~27  _  3  8  / 1  _  fJ:  _  1 
V  64  —  ^34  4’\8  2' 

Otherwise,  the  fraction  may  be  reduced  to  a  decimal,  ai 
the  cube  root  of  this  found. 

The  general  method  of  extracting  cube  root  is  so  similar 
that  for  extracting  square  root,  which  was  quite  fully  show 
that  no  further  explanation  is  necessary. 


HIGHER  ROOTS. 

The  fourth  root  of  a  number  may  be  found  by  ext’.actii 
the  square  root  of  the  square  root  of  the  number ;  thus, 

I4/  256  =  V  V  256  =  l/l6  =  4. 

The  sixth  root  of  a  number  maybe  found  by  extracting  tl 
square  root  of  the  cube  root,  or  the  cube  root  of  the  squai 
root;  thus, 

y  64  —  l/  -]/  64  =  8  =  2. 

The  general  formula  for  extracting  any  root  is 


Root  = 


I) 


+ 


n 


1 


R, 


n  X  Rn~l  n 
in  which  n  is  the  index  of  the  root  sought,  D  the  trial  div 
dend,  and  R  the  trial  root.  For  example, 

I)  .  3  „„„  .  I) 


Fourth  root  = 


+  fifth  root  -  +  1  B. 


These  roots  are  to  be  found  by  the  same  general  metho< 
explained  for  square  and  cube  roots. 


SQUARE  ROOTS  AND  CUBE  ROOTS. 


13 


SQUARE  ROOTS  AND  CUBE  ROOTS. 


Table  of  Square  Roots  and  Cube  Roots,  of  Numbers 

.  From  1  to  1,005. 

Note. — Wherever  the  effect  of  a  fourth  decimal  in  the 
following  roots  would  be  to  add  1  to  the  third  and  final  deci¬ 
mal  in  the  table,  the  addition  has  been  made. 


No. 

Sq.  Rt. 

C.  Rt. 

NO. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

1 

1.000 

1.000 

31 

5.568 

3.141 

61 

7.810 

3.936 

*  2 

1.414 

1.260 

32 

5.657 

3.175 

62 

7.874 

3.958 

3 

1.732 

1.442 

33 

5.745 

3.207 

63 

7.937 

3.979 

4 

2.000 

1.587 

34 

5.831 

3.240 

64 

8.000 

4.000 

5 

2.236 

1.710 

35 

5.916 

3.271 

65 

8.062 

4.021 

6 

2.449 

1.817 

36 

6.000 

8.302 

66 

8.124 

4.041 

7 

2.646 

1.913 

37 

6.083 

3.332 

67 

8.185 

4.061 

8 

2.828 

2.000 

38 

6.164 

3.362 

68 

8.246 

4.082 

9 

3.000 

2.080 

39 

6.245 

3.391 

69 

8.307 

4.102 

10 

3.162 

2.154 

40 

6.325 

3.420 

70 

8.367 

4.121 

11 

3.317 

2.224 

41 

6.403 

3.448 

71 

8.426 

4.141 

12 

3.464 

2.289 

42 

6.481 

3.476 

72 

8.485 

4.160 

13 

3.606 

2.351 

43 

6.557 

3.503 

73 

8.544 

4.179 

14 

3.742 

2.410 

44 

6.633 

3.530 

74 

8.602 

4.198 

15 

3.873 

2.466 

45 

6.708 

3.557 

75 

8.660 

4.217 

16 

4.000 

2.520 

46 

6.782 

3.583 

76 

8.718 

4.236 

17 

4.123 

2.571 

47 

6.856 

3.609 

77 

8.775 

4.254 

18 

4.243 

2.621 

48 

6.928 

3.634 

78 

8.832 

4.273 

19 

4.359 

2.668 

49 

7.000 

3.659 

79 

8.888 

4.291 

20 

4.472 

2.714 

50 

7.071 

3.684 

80 

8.944 

4.309 

21 

4.583 

2.759 

51 

7.141 

3.708 

81 

9.000 

4,327 

22 

4.690 

2.802 

52 

7.211 

3.732 

82 

9.055 

4.344 

23 

4.796 

2.844 

53 

7.280 

3.756 

83 

9.110 

4.362 

24 

4.899 

2.884 

54 

7.348 

3.780 

84 

9.165 

4.379 

25 

5.000 

2.924 

55 

7.416 

3.803 

85 

9.219 

4.397 

26 

5.099 

2.962 

56 

7.483 

3.826 

86 

9.274 

4.414 

27 

5.196 

3.000 

57 

7.550 

3.848 

87 

9.327 

4.431 

28 

5.291 

3.037 

58 

7.616 

3.871 

88 

9.381 

4.448 

29 

5.385 

3.072 

59 

7.681 

3.893 

89 

9.434 

4.465 

30 

5.477 

3.107 

60 

7.746 

3.915 

90 

9.487 

4.481 

B 


14 


ARITHMETIC. 


Table— ( Continued). 


No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt, 

C.  Rt. 

91 

9.539 

4.498 

131 

11.445 

5.079 

171 

13.077 

5.550 

92 

9.592 

4.514 

132 

11.489 

5.092 

172 

13.115 

5.561 

93 

9.644 

4.531 

133 

11.533 

5.104 

173 

13.153 

5.572 

94 

9.695 

4.547 

134 

11.576 

5.117 

174 

13.191 

5.583 

95 

9.747 

4.563 

135 

11.619 

5.130 

175 

13.229 

5.593 

96 

9.798 

4.579 

136 

11.662 

5.143 

176 

13.266 

5.604 

97 

9.849 

4.595 

137 

11.705 

5.155 

177 

13.304 

5.615 

98 

9.899 

4.610 

138 

11.747 

5.168 

178 

13.342 

5.625 

99 

9.950 

4.626 

139 

11.790 

5.180 

179 

13.379 

5.636 

100 

10.000 

4.642 

140 

11.832 

5.192 

180 

13.416 

5.646 

101 

10.050 

4.657 

141 

11.874 

5.205 

181 

13.454 

5.657 

102 

10.099 

4.672 

142 

11.916 

5.217 

182 

13.491 

5.667 

103 

10.149 

4.687 

143 

11.958 

5.229 

183 

13.528 

5.677 

104 

10.198 

4.703 

144 

12.000 

5.241 

184 

13.565 

5.688 

105 

10.247 

4.718 

145 

12.042 

5.254 

185 

13.601 

5.698 

106 

10.296 

4.733 

146 

12.083 

5.266 

186 

13.638 

5.708 

107 

10.344 

4.747 

147 

12.124 

5.278 

187 

13.675 

5.718 

108 

10.392 

4.762 

148 

12.165 

5.290 

188 

13.711 

5.729 

109 

10.440 

4,777 

149 

12.207 

5.301 

189 

13.748 

5.739 

110 

10.488 

4.791 

150 

12.247 

5.313 

190 

13.784 

5.749 

111 

10.536 

4.806 

151 

12.288 

5.325 

191 

13.820 

5.759 

112 

10.583 

4.820 

152 

12.329 

5.337 

192 

13.856 

5.769 

113 

10.630 

4.835 

153 

12.369 

5.348 

193 

13.892 

5.779 

114 

10.677 

4.849 

154 

12.410 

5.360 

194 

13.928 

5.789 

115 

10.724 

4.863 

155 

12.450 

5.372 

195 

13.964 

5.799 

116 

10.770 

4.877 

156 

12.490 

5.383 

196 

14.000 

5.809 

117 

10.817 

4.891 

157 

12.530 

5.395 

197 

14.036 

5.819 

118 

10.863 

4.905 

158 

12.570 

5.406 

198 

14.071 

5.828 

119 

10.909 

4.919 

159 

12.609 

5.417 

199 

14.107 

5.838 

120 

10.954 

4.932 

160 

12.649 

5.429 

200 

14.142 

5.848 

121 

11.000 

4.946 

161 

12.689 

5.440 

201 

14.177 

5.858 

122 

11.045 

4.9(50 

162 

12.728 

5.451 

202 

14.213 

5.867 

123 

11.090 

4.973 

163 

12.767 

5.463 

203 

14.248 

5.877 

124 

11.135 

4.987 

164 

12.806 

5.474 

201 

14.283 

5.887 

125 

11.180 

5.000 

165 

12.8-15 

5.485 

205 

14.318 

5.896 

126 

11.225 

5.013 

166 

12.884 

5.496 

206 

14.353 

5.906 

127 

11.269 

5.026 

167 

12.923 

5.507 

207 

14.387 

5.915 

128 

11.314 

5.040 

168 

12.961 

5.518 

208 

14.422 

5.925 

129 

11.358 

5.053 

169 

13.000 

5.529 

209 

14.457 

5.934 

130 

11.402 

5.066 

170 

13.038 

5.540 

210 

14.491 

5.944 

SQUARE  ROOTS  AND  CURE  ROOTS. 


15 


Table — ( Continued). 


No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

211 

14.526 

5.953 

251 

15.843 

6.308 

291 

17.059 

6.627 

212 

14.560 

5.963 

252 

15.874 

6.316 

292 

17.088 

6.634 

213 

14.594 

5.972 

253 

15.906 

6.325 

293 

17.117 

6.642 

214 

14.629 

5.981 

254 

15.937 

6.333 

294 

17.146 

6.649 

215 

14.663 

5.991 

255 

15.969 

6.341 

295 

17.176 

6.657 

216 

14.697 

6.  tioo 

256 

16.000 

6.350 

296 

17.205 

6.664 

217 

14.731 

6.009 

257 

16.031 

6.358 

297 

17.234 

6.672 

218 

14.765 

6.018 

258 

16.062 

6.366 

298 

17.263 

6.679 

219 

14.799 

6.028 

259 

16.093 

6.374 

299 

17.292 

6.687 

220 

14.832 

6.037 

260 

16.124 

6.382 

300 

17.320 

6.694 

221 

14.866 

6.046 

261 

16.155 

6.391 

301 

17.349 

6.702 

222 

14.900 

6.055 

262 

16.186 

6.399 

302 

17.378 

6.709 

223 

14.933 

6.064 

263 

16.217 

6.407 

303 

17.407 

6.717 

224 

14.967 

6.073 

264 

16.248: 

6.415 

304 

17.436 

6.724 

225 

15.000 

6.082 

265 

16.279 

6.423 

305 

17.464 

6.731 

226 

15.033 

6.091 

266 

.16.309 

6.431 

306 

17.493 

6.739 

227 

15.066 

6.100 

267 

16.340 

6.439 

307 

17.521 

6.746 

228 

15.100 

6.109 

268 

16.371 

6.447 

308 

17.550 

6.753 

229 

15.138 

6.118 

269 

16.401 

6.455 

309 

17.578 

6.761 

230 

15.166 

6.127 

270 

16.432 

6.463 

310 

17.607 

6.768 

231 

15.199 

6.136 

271 

16.462 

6.471 

311 

17.635 

6.775 

232 

15.231 

6.145 

272 

16.492 

6.479 

312 

17.663 

6.782 

233 

15.264 

6.153 

273 

16.523 

6.487 

313 

17.692 

6.790 

234 

15.297 

6.162 

274 

16.553 

6.495 

314 

17.720 

6.797 

235 

15.330 

6.171 

275 

16.583 

6.503 

315 

17.748 

6.804 

236 

15.362 

6.180 

276 

16.613 

6.511 

316 

17.776 

6.811 

237 

15.395 

6.188 

277 

16.643 

6.519 

317 

17.804 

6.818 

238 

15.427 

6.197. 

278 

16.673 

6.526 

318 

17.833 

6.826 

239 

15.460 

6.206 

279 

16.703 

6.534 

319 

17.861 

6.833 

240 

15.492 

6.214 

280 

16.733 

6.542 

320 

17.888 

6.840 

241 

15.524 

6.223 

281 

16.763 

6.550 

321 

17.916 

6.847 

242 

15.556 

6.232 

282 

16.793 

6.558 

322 

17.944 

6.854 

243 

15.588 

6.240 

283 

16.823 

6.565 

323 

17.972 

6.861 

244 

15.620 

6.249 

284 

16.852 

6.573 

324 

18.000 

6.868 

245 

15.652 

6.257 

285 

16.882 

6.581 

325 

18.028 

6.875 

246 

15.684 

6.266 

286 

16.911 

6.588 

326 

18.055 

6.882 

247 

15.716 

6.274 

287 

16.941 

6.596 

327 

18.083 

6.889 

248 

15.748 

6.283 

288 

16.971 

6.604 

328 

18.111 

6.896 

249 

15.780 

6.291 

289 

17.000 

6.611 

329 

18.138 

6.903 

250 

15.811 

6.300 

290 

17.029 

6.619 

330 

18.166 

6.910 

16 


ARITHMETIC. 


Table — ( Continued). 


No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

331 

18.193 

6.917 

371 

19.261 

7.185 

411 

20.273 

7.435 

332 

18.221 

6.924 

372 

19.287 

7.192 

412 

20.298 

7.441 

333 

18.248 

6.931 

373 

19.313 

7.198 

413 

20.322 

7.447 

334 

18.276 

6.938 

374 

19.339 

7.205 

414 

20.347 

7.453 

335 

18.303 

6.945 

375 

19.365 

7.211 

415 

20.371 

7.459 

336 

18.330 

6.952 

376 

19.391 

7.218 

416 

20.396 

7.465 

337 

18.358 

6.959 

377 

19.416 

7.224 

417 

20.421 

7.471 

338 

18.385 

6.966 

378 

19.442 

7.230 

418 

20.4-15 

7.477 

339 

18.412 

6.973 

379 

19.468 

7.237 

419 

20.469 

7.483 

340 

18.439 

6.979 

380 

19.494 

7.243 

420 

20.494 

7.489 

341 

18.466 

6.986 

381 

19.519 

7.249 

421 

20.518 

7.495 

342 

18.493 

6.993 

382 

19.545 

7.256 

422 

20.543 

7.501 

343 

18.520 

7.000 

383 

19.570 

7.262 

423 

20.567 

7.507 

344 

18.547 

7.007 

384 

19.596 

7.268 

424 

20.591 

7.513 

345 

18.574 

7.014 

385 

19.621 

7.275 

425 

20.615 

7.518 

346 

18.601 

7.020 

386 

19.647 

7.281 

426 

20.640 

7.524 

347 

18.628 

7.027 

387 

19.672 

7.287 

427 

20.664 

7.530 

348 

18.655 

7.034 

388 

19.698 

7.294 

428 

20.688 

7.536 

349 

18.681 

7.041 

389 

19.723 

7.300 

429 

20.712 

7.542 

350 

18.708 

7.047 

390 

19.748 

7.306 

430 

20.736 

7.548 

351 

18.735 

7.054 

391 

19.774 

7.312 

431 

20.760 

7.554 

352 

18.762 

7.061 

392 

19.799 

7.319 

432 

20.785 

7.559 

353 

18.788 

7.067 

393 

19.824 

7.325 

433 

20.809 

7.565 

354 

18.815 

7.074 

394 

19.849 

7.331 

434 

20.833 

7.571 

355 

18.841 

7.081 

395 

19.875 

7.337 

435 

20.857 

7.577 

356 

18.868 

7.087 

396 

19.900 

7.343 

436 

20.881 

7.583 

357 

18.89-1 

7.094 

397 

19.925 

7.350 

437 

20.904 

7.589 

358 

18.921 

7.101 

398 

19.950 

7.356 

438 

20.928 

7.594 

359 

18.947 

7.107 

399 

19.975 

7.362 

439 

20.952 

7.600 

360 

18.974 

7.114 

400 

20.000 

7.368 

440 

20.976 

7.606 

361 

19.000 

7.120 

401 

20.025 

7.374 

441 

21.000 

7.612 

362 

19.026 

7.127 

402 

20.050 

7.380 

442 

21.024 

7.617 

363 

19.053 

7.133 

403 

20.075 

7.386 

443 

21.048 

7.623 

364 

19.079 

7.140 

404 

20.100 

7  392 

444 

21.071 

7.629 

365 

19.105 

7.147 

405 

20.125 

7.399 

445 

21.095 

7.635 

366 

19.131 

7.153 

406 

20.149 

7.405 

446 

21.119 

7.640 

367  • 

19.157 

7.160 

407 

20.174 

7.411 

447 

21.142 

7.646 

368  , 

19.183 

7.166 

408 

20.199 

7.417 

44S 

21.166 

7.652 

369  , 

19.209 

7.173 

409 

20.224 

7.428 

119 

21.190 

7.657 

370  ‘ 

19.235 

7.179 

410 

20.248 

7.429 

450 

21.213 

7.663 

No. 

451 

452 

453 

454 

455 

456 

457 

458 

459 

460 

461 

462 

463 

464 

465 

466 

467 

468 

469 

470 

471 

472 

473 

474 

475 

476 

477 

478 

479 

480 

481 

482 

483 

484 

485 

486 

487 

488 

489 

490 


SQUARE  ROOTS  AND  CUBE  ROOTS. 


17 


Table— ( Continued).. 


C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

7.669 

491 

22.158 

7.889 

531 

23.043 

8.098 

7.674 

492 

22.181 

7.894 

532 

23.065 

8.103 

7.680 

493 

22.204 

7.900 

533 

23.087 

8.108 

7.686 

494 

22.226 

7.905 

534 

23.108 

8.113 

7.691 

495 

22.249 

7.910 

536 

23.130 

8.118 

7.697 

496 

22.271 

7.916 

536 

23.152 

8.123 

7.703 

497 

22.293 

7.921 

537 

23.173 

8.128 

7.708 

498 

22.316 

7.926 

538 

23.195 

8.133 

7.714 

499 

22.338 

7.932 

539 

23.216 

8.138 

7.719 

500 

22.361 

7.937 

540 

23.238 

8.143 

7.725 

501 

22.383 

7.942 

541 

23.259 

8.148 

7.731 

502 

22.405 

7.948 

542 

23.281 

8.153 

7.736 

503 

22.428 

7.953 

543 

23.302 

8.158 

7.742 

504 

22.450 

7.958 

544 

23.324 

8.163 

7.747 

505 

22.472 

7.963 

545 

23.345 

8.168 

7.753 

506 

22.494 

7.969 

546 

23.367 

8.173 

7.758 

507 

22.517 

7.974 

547 

23.388 

8.178 

7.764 

508 

22.539 

7.979 

548 

23.409 

8.183 

7.769 

509 

22.561 

7.984 

549 

23.431 

8.188 

7.775 

510 

22.583 

7.990 

550 

23.452 

8.193 

7.780 

511 

22.605 

7.995 

551 

23.473 

8.198 

7.786 

512 

22.627 

8.000 

552 

23.495 

8.203 

7.791 

513 

22.649 

8.005 

553 

23.516 

8.208 

7.797 

514 

22.672 

8.010 

554 

23.537 

8.213 

7.802 

515 

22.694 

8.016 

555 

23.558 

8.218 

7.808 

516 

22.716 

8.021 

556 

23.580 

8.223 

7.813 

517 

22.738 

8.026 

557 

23.601 

8.228 

7.819 

518 

22.760 

8.031 

558 

23.622 

8.233 

7.824 

519 

22.782 

8.036 

559 

23.643 

8.238 

7.830 

520 

22.803 

8.041 

560 

23.664 

8.243 

7.835 

521 

22.825 

8.047 

561 

23.685 

8.247 

7.841 

622 

22.847 

8.052 

562 

23.706 

8.252 

7.846 

523 

22.869 

8.057 

563 

23.728 

8.257 

7.851 

524 

22.891 

8.062 

564 

23.749 

8.262 

7.857 

525 

22.913 

8.067 

565 

23.770 

8.267 

7.862 

526 

22.935 

8.072 

566 

23.791 

8.272 

7.868 

527 

22.956 

8.077 

567 

23.812 

8.277 

7.873 

528 

22.978 

8.082 

568 

23.833 

8.282 

7.878 

529 

23.000 

8.088 

569 

23.854 

8.286 

7.884 

530 

23.022 

8.093 

570 

23.875 

8.291 

18 


ARITHMETIC. 


Table — ( Continued). 


No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

571 

23.896 

8.296 

611 

24.718 

8.486 

651 

25.515 

8.667 

572 

23.916 

8.301 

612 

24.739 

8.490 

652 

25.534 

8.671 

573 

23.937 

8.306 

613 

24.759 

8.495 

653 

25.554 

8.676 

574 

23.958 

8.311 

614 

24.779 

8.499 

654 

25.573 

8.680 

575 

23.979 

8.315 

615 

24.799 

8.504 

655 

25.593 

8.684 

576 

24.000 

8.320 

616 

24.819 

8.509 

656 

25.612 

8.689 

577 

24.021 

8.325 

617 

24.839 

8.513 

657 

25.632 

8.693 

578 

24.042 

8.330 

618 

24.860 

8.518 

658 

25.651 

8.698 

579 

24.062 

8.335 

619 

24.880 

8.522 

659 

25.671 

8.702 

580 

24.083 

8.340 

620 

24.900 

8.527 

660 

25.690 

8.707 

581 

24.104 

8.344 

621 

24.920 

8.532 

661 

25.710 

8.711 

582 

24.125 

8.349 

622 

24.940 

8.536 

662 

25.729 

8.715 

583 

24.145 

8,354 

623 

24.960 

8.541 

663 

25.749 

8.720 

584 

24.166 

8.359 

624 

24.980 

8.545 

664 

25.768 

8.724 

585 

24.187 

8.363 

625 

25.000 

8.550 

665 

25.788 

8.728 

586 

24.207 

8.368 

626 

25.020 

8.554 

666 

25.807 

8.733 

587 

24.228 

8.373 

627 

25.040 

8.559 

667 

25.826 

8.737 

588 

24.249 

8.378 

628 

25.060 

8.563 

668 

25.846 

8.742 

589 

24.269 

8.382 

629 

25.080 

8.568 

669 

25.865 

8.746 

590 

24.290 

8.387 

630 

25.100 

8.573 

670 

25.884 

8.750 

591 

24.310 

8.392 

631 

25.120 

8.577 

671 

25.904 

8.755 

592 

24.331 

8.397 

632 

25.140 

8.582 

672 

25.923 

8.759 

593 

24.352 

8.401 

633 

25.159 

8.586 

673 

25.942 

8.763 

594 

24.372 

8.406 

634 

25.179 

8.591 

674 

25.961 

8.768 

595 

24.393 

8.411 

635 

25.199 

8.595 

675 

25.981 

8.772 

596 

24.413 

8.415 

636 

25.219 

8.600 

676 

26.000 

8.776 

597 

24.434 

8.420 

637 

25.239 

8.604 

677 

26.019 

8.781 

598 

24.454 

8.425 

638 

25.259 

8.609 

678 

26.038 

8.785 

599 

24.474 

8.430 

639 

25.278 

8.613 

679 

26.058 

8.789 

600 

24.495 

8.434 

640 

25.298 

8.618 

680 

26.077 

8.794 

601 

24.515 

8.439 

641 

25.318 

8.622 

681 

26.096 

8.798 

602 

24.536 

8.444 

642 

25.338 

8.627 

682 

26.115 

8.802 

603 

24.556 

8.448 

643 

25.357 

8.631 

683 

26.134 

8.807 

604 

24.576 

8.453 

644 

25.377 

8.636 

684 

26.153 

8.811 

605 

24.597 

8.458 

645 

25.397 

8.640 

685 

26.172 

8.815 

606 

24.617 

8.462 

646 

25.416 

8.645 

686 

26.192 

8.819 

607 

24.637 

8.467 

647 

25.436 

8.(549 

687 

26.211 

8.824 

608 

24.658 

8.472 

648 

25.456 

8.653 

688 

26.230 

8.828 

609 

24.678 

8.476 

649 

25.475 

8.658 

689 

26.249 

8.832 

610 

24.698 

8.481 

650 

25.495 

8.662 

690 

26.268 

8.837 

SQUARE  ROOTS  AND  CUBE  ROOTS. 


IS 


Table — ( Continued). 


No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

691 

26.287 

8.841 

731 

27.037 

9.008 

771 

27.767 

9.170 

692 

26.306 

8.845 

732 

27.055 

9.012 

772 

27.785 

9.174 

693 

26.325 

8.849 

733 

27.074 

9.016 

773 

27.803 

9.177 

694 

26.344 

8.854 

734 

27.092 

9.020 

774 

27.821 

9.181 

695 

26.363 

8.858 

735 

27.111 

9.025 

775 

27.839 

9.185 

696 

26.382 

8.862 

736 

27.129 

9.029 

776 

27.857 

9.189 

697 

26.401 

8.866 

737 

27.148 

9.033 

777 

27.875 

9.193 

698 

26.420 

8.871 

738 

27.166 

9.037 

778 

27.893 

9.197 

699 

26.439 

8.875 

739 

27.185 

9.041 

779 

27.911 

9.201 

700 

26.457 

8.879 

740 

27.203 

9.045 

780 

27.928 

9.205 

701 

26.476 

8.883 

741 

27.221 

9.049 

781 

27.946 

9.209 

702 

26.495 

8.887 

742 

27.240 

9.053 

782 

27.964 

9.213 

703 

26.514 

8.892 

743 

27.258 

9.057 

783 

27.982 

9.217 

704 

26.533 

8.896 

744 

27.276 

9.061 

784 

28.000 

9.221 

705 

26.552 

8.900 

745 

27.295 

9.065 

785 

28.018 

9.225 

706 

26.571 

8.904 

746 

27.313 

9.069 

786 

28.036 

9.229 

707 

26.589 

8.908 

747 

27.331 

9.073 

787 

28.053 

9.233 

708 

26.608 

8.913 

748 

27.350 

9.077 

788 

28.071 

9.236 

709 

26.627 

8.917 

749 

27.368 

9.082 

789 

28.089 

9.240 

710 

26.646 

8.921 

750 

27.386 

9.086 

790 

28.107 

9.244 

711 

26.665 

8.925 

751 

27.404 

9.090 

791 

28.125 

9.248 

712 

26.683 

8.929 

752 

27.423 

9.094 

792 

28.142 

9.252 

713 

26.702 

8.934 

753 

27.441 

9.098 

793 

28.160 

9.256 

714 

26.721 

8.938 

754 

27.459 

9.102 

794 

28.178 

9.260 

715 

26.739 

8.942 

755 

27.477 

9.106 

795 

28.196 

9.264 

716 

26.758 

8.946 

756 

27.495 

9.110 

796 

28.213 

9.268 

717 

26.777 

8.950 

757 

27.514 

9.114 

797 

28.231 

9.272 

718 

26.795 

8.954 

758 

27.532 

9.118 

798 

28.249 

9.275 

719 

26.814 

8.959 

759 

27.550 

9.122 

799 

28.267 

9.279 

720 

26.833 

8.963 

760 

27.568 

9.126 

800 

28.284 

9.283 

721 

26.851 

8.967 

761 

27.586 

9.130 

801 

28.302 

9.287 

722 

26.870 

8.971 

762 

27.604 

9.134 

802 

28.320 

9.291 

723 

26.889 

8.975 

763 

27.622 

9.138 

803 

28.337 

9.295 

724 

26.907 

8.979 

764 

27.640 

9.142 

804 

28.355 

9.299 

725 

26.926 

8.983 

765 

27.659 

9.146 

805 

28.372 

9.302 

726 

26.944 

8.988 

766 

27.677 

9.150 

806 

28.390 

9.306 

727 

26.963 

8.992 

767 

27.695 

9.154 

807 

28.408 

9.310 

728 

26.981 

8.996 

768 

27.713 

9.158 

808 

28.425 

9.314 

729 

27.000 

9.000 

769 

27.731 

9.162 

809 

28.443 

9.318 

730 

27.018 

9.004 

770 

27.749 

9.166 

810 

28.460 

9.322 

20 


ARITHMETIC. 


Table — ( Continued ) . 


No. 

Sq.  Rt. 

C.  Rt. 

NO. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt.1 

C.  Rt. 

811 

28.478 

9.325 

851 

29.172 

9.476 

891 

29.850 

9.623 

812 

28.496 

9.329 

852 

29.189 

9.480 

892 

29.866 

9.626 

813 

28.513 

9.333 

853 

29.206 

9.484 

893 

29.883 

9.630 

814 

28.531 

9.337 

an 

29.223 

9.487 

894 

29.900 

9.633 

815 

28.548 

9.341 

855 

29.240 

9.491 

895 

29.917 

9.637 

816 

28.566 

9.345 

856 

29.257 

9.495 

896 

29.933 

9.641 

817 

28.583 

9.348 

857 

29.275 

9.499 

897 

29.950 

9.644 

818 

28.601 

9.352 

858 

29.292 

9.502 

898 

29.967 

9.648 

819 

28.618 

9.356 

859 

29.309 

9.506 

899 

29.983 

9.651 

820 

28.636 

9.360 

860 

29.326 

9.510 

900 

30.000 

9.655 

821 

28.653 

9.364 

861 

29.343 

9.513 

901 

30.017 

9.658 

822 

28.670 

9.367 

862 

29.360 

9.517 

902 

30.033 

9.662 

823 

28.688 

9.371 

863 

29.377 

9.521 

903 

30.050 

9.666 

824 

28.705 

9.375 

864 

29.394 

9.524 

904 

30.067 

9.669 

825 

28.723 

9.379 

865 

29.411 

9.528 

905 

30.083 

9.673 

826 

28.740 

9.383 

866 

29.428 

9.532 

906 

30.100 

9.676 

827 

28.758 

9.386 

867 

29.445 

9.535 

907 

30.116 

9.680 

828 

28.775 

9.390 

868 

29.462 

9.539 

908 

30.133 

9.683 

829 

28.792 

9.394 

869 

29.479 

9.543 

909 

30.150 

9.687 

830 

28.810 

9.398 

870 

29.496 

9.546 

910 

30.166 

9.690 

831 

28.827 

9.402 

871 

29.513 

9.550 

911 

30.183 

9.694 

832 

28.844 

9.405 

872 

29.530 

9.554 

912 

30.199 

9.698 

833 

28.862 

9.409 

873 

29.547 

9.557 

913 

30.216 

9.701 

834 

28.879 

9.413 

874 

29.563 

9.561 

914 

30.232 

9.705 

835 

28.896 

9.417 

875 

29.580 

9.565 

915 

30.249 

9.708 

836 

28.914 

9.420 

876 

29.597 

9.568 

916. 

30.265 

9.712 

837 

28.931 

9.424 

877 

29.614 

9.572 

917 

30.282 

9.715 

838 

28.948 

9.428 

878 

29.631 

9.576 

918 

30.298 

9.719 

839 

28.965 

9.432 

879 

29.648 

9.579 

919 

30.315 

9.722 

840 

28.983 

9.435 

880 

29.665 

9.583 

920 

30.331 

9.726 

841 

29.000 

9.439 

881 

29.682 

9.586 

921 

30.348 

9.729 

842 

29.017 

9.443 

882 

29.698 

9.590 

922 

30.364 

9.733 

843 

29.034 

9.447 

883 

29.715 

9.594 

923 

30.381 

9.736 

844 

29.052 

9.450 

884 

29.732 

9.597 

924 

30.397 

9.740 

845 

29.069 

9.454 

885 

29.749 

9.601 

925 

30.414 

9.743 

846 

29.086 

9.458 

886 

29.766 

9.605 

926 

30.430 

9.747 

847 

29.103 

9.461 

887 

29.782 

9.608 

927 

30.447 

9.750 

848 

29.120 

9.465 

888 

29.7*9 

9.612 

928 

30.463 

9.754 

849 

29.138 

9.469 

889 

29.816 

9.615 

929 

30.479 

9.757 

850 

29.155 

1  9.473 

890 

29.833 

9.619 

930 

30.496 

9.761 

SQUARE  ROOTS  AND  CUBE  ROOTS. 


21 


Table— ( Continued). 


No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

931 

30.512 

9.764 

956 

30.919 

9.851 

981 

31.321 

9.936 

932 

30.529 

9.768 

957 

30.935 

9.855 

982 

31.337 

9.940 

933 

30.545 

9.771 

958 

30.952 

9.858 

983 

31.353 

9.943 

934 

30.561 

9.775 

959 

3(1968 

9.861 

984 

31.369 

9.946 

935 

30.578 

9  778 

960 

30.984 

9.865 

985 

31.385 

9.950 

936 

30.594 

9.782 

961 

31.000 

9.868 

986 

31.401 

9.953 

937 

30.610 

9.785 

962 

31.016 

9.872 

987 

31.417 

9.956 

938 

30.627 

9.789 

963 

31.032 

9.875 

988 

31.432 

9.960 

939 

30.643 

9.792 

964 

31.048 

9.878 

989 

31.448 

9.963 

940 

30.659 

9.796 

965 

31.064 

9.882 

990 

31.464 

9.967 

941 

30.676 

9.799 

966 

31.080 

9.885 

991 

31.480 

9.970 

942 

30.692 

9.803 

967 

31.097 

9.889 

992 

31.496 

9.973 

943 

30.708 

9.806 

968 

31.113 

9.892 

993 

31.512 

9.977 

944 

30.725 

9.810 

969 

31.129 

9.896 

994 

31.528 

9.980 

945 

30.741 

9.813 

970 

31.145 

9.899 

995 

31.544 

9.983 

946 

30.757 

9.817 

971 

31.161 

9.902 

996 

31.559 

9.987 

947 

30.773 

9.820 

972 

31.177 

9.906 

997 

31.575 

9.990 

948 

30.790 

9.824 

973 

31.193 

9.909 

998 

31.591 

9.993 

949 

30.806 

9.827 

974 

31.209 

9.913 

999 

31.607 

9.997 

950 

30.822 

9.830 

975 

31.225 

9.916 

1000 

31.623 

10.000 

951 

30.838 

9.834 

976 

31.241 

9.919 

1001 

31.639 

10.003 

952 

30.854 

9.837 

977 

31.257 

9.923 

1002 

31.654 

10.006 

953 

30.871 

9.841 

978 

31.273 

9.926 

1003 

31.670 

10.010 

954 

30.887 

9.844 

979 

31.289 

9.929 

1004 

31.686 

10.013 

955 

30.903 

9.848 

980 

31.305 

9.933 

1005 

31.702 

10.017 

The  square  root  of  any  number  from  .01  to  10.05,  advan¬ 
cing  by  .01,  may  be  found  by  moving  the  decimal  place  in 

the  Sq.  Rt.  column  one  place  to  the  left ;  thus,  ~/ 9.48  =  3.079. 
The  cube  root  of  any  number  from  .001  to  1.005,  advancing 
by  .001,  may  be  found  by  moving  the  decimal  point  in  the 

C.  Rt.  column  one  place  to  the  left;  thus,  1^.816  =  .9345. 

The  approximate  squares  of  numbers  from  1  to  31.7,  and 
cubes  from  1  to  10,  may  be  found,  also.  Required,  the  square 
of  30.53  :  In  the  Sq.  Rt.  column,  find  30.529  ;  932  is,  then,  the 
approximate  square  of  30.53.  Required,  the  cube  of  9.8 :  Find 
in  theC.  Rt.  column  9.799  ;  then,  the  approximate  cube  is  941, 


22 


WEIGHTS  AND  MEASURES. 


WEIGHTS  AND  MEASURES. 


LINEAR  MEASURE. 


12  inches  (in.) . 

...  =  1  foot  . 

. ft. 

3  feet  . 

....  =  1  yard . 

. yd. 

5.5  yards  . 

...  ==  l  rod  . 

. rd. 

40  rods . 

....  =  1  furlong . 

. fur. 

8  furlongs . 

...  =  1  mile  . 

. mi. 

in. 

ft. 

yd.  rd.  fur.  mi. 

36  = 

3  = 

1 

198  = 

16.5  = 

5.5  =  1 

7,920  = 

660  = 

220  =  40  =  1 

63,360  = 

5,280  = 

1,760  =  320  8  =  1 

SURVEYOR'S  MEASURE. 

7.92  inches . 

....  =  1  link  . 

. li. 

25  links . 

....  =  1  rod . 

. rd. 

4  rods  4 

100  links  >  . 

....  =  1  chain  . 

ch. 

66  feet  j 

80  chains . 

....  -  1  mile . 

1  mi.  -  80  ch.  =  320  rd.  =  8,000  li.  =  63,360  in. 


SQUARE  MEASURE. 


144  square  inches  (sq.  in.). 

9  square  feet . 

30y  square  yards . 

160  square  rods  . . 

640  acres . 

sq.  mi.  A.  sq.  rd. 

1  =  640  =  102,400 


=  1  square  foot . sq.  ft. 

=  1  square  yard . sq.  yd. 

=  1  square  rod . sq.  rd. 

=  1  acre  . A. 

=  ^square  mile . sq.  mi. 


sq.  yd.  sq.  ft.  sq.  in. 

=  3,097,600  =  27,878,400  =  4,014,489,600 


TABLES. 


23 


SURVEYOR’S  SQUARE  MEASURE. 

625  square  links  (sq.  li.)  . =  1  square  rod . sq.  rd. 

16  square  rods .  =  1  square  chain  . sq.  ch. 

10  square  chains .  =  1  acre . A. 

640  acres .  =  1  square  mile . sq.  mi. 

36  square  miles  (6  mi.  square)  =  1  township . Tp. 

1  sq.  mi.  =  640  A.  =  6,400  sq.  ch.  =  102,400  sq.  rd. 

=  64,000,000  sq.  li. 

The  acre  contains  4,840  sq.  yd.,  or  43,560  sq.  ft.,  and  in 
form  of  a  square  is  208.71  ft.  on  a  side. 


CUBIC  MEASURE. 


1,728  cubic  inches  (cu.  in.) . =  1  cubic  foot  ... 

27  cubic  feet  .  =  1  cubic  yard.... 

128  cubic  feet  . =  1  cord . 

24$  cubic  feet .  =  1  perch  . 

1  cu.  yd.  =  27  cu.  ft.  =  46,656  cu.  in. 


cu.  ft. 


cu.yd. 
. cd. 

. P. 


MEASURE  OF  ANGLES  OR  ARCS. 

60  seconds  (") . =  1  minute  . ' 

60  minutes  . =  1  degree  . 0 

90  degrees . =  1  rt.  angle  or  quadrant  □ 

360  degrees . =  1  circle . cir. 

1  cir.  =  360°  =  21,600'  =  1,296,000" 


AVOIRDUPOIS  WEIGHT. 

437.5  grains  (gr.) . =  1  ounce . oz. 

16  ounces  .  =  1  pound  . lb. 

100  pounds . =  1  hundredweight  . cwt. 

20  cwt.,  or  2,0001b . —  1  ton . T. 

IT.  =  20  cwt.  =  2,000  1b.  =  32,000  oz.  =  14,000,000 gr. 
The  avoirdupois  pound  contains  7,000  grains. 

LONG  TON  TABLE. 

16  ounces  . .  =  1  pound . 

112  pounds .  =  1  hundredweight 

20  cwt.,  or  2,240  lb .  =  1  ton . 


...lb. 

cwt. 

...T. 


24 


WEIGHTS  AND  MEASURES. 


TROY  WEIGHT. 

24  grains  (gr.)  .  =  1  pennyweight  . pwt. 

20  pennyweights . =  1  ounce . oz. 

12  ounces .  =  l  pound . lb. 

1  lb.  =  12  oz.  =  240  pwt.  =  5,760  gr. 


DRY  MEASURE. 

2  pints  (pt.)  .  =  1  quart  . qt. 

8  quarts  . =  1  peck  . pk. 

4  peeks . =  1  bushel  . bu 

1  bu.  =  4  pk.  =  32  qt.=  64  pt. 

The  U.  S.  struck  bushel  contains  2,150.42  cu.  in.  =  1.2444 
cu.  ft.  Its  dimensions  are,  by  law,  18£  in.  in  diameter  and 
8  in.  deep.  The  heaped  bushel  is  equal  to  if  struck  bushels, 
the  cone  being  6  in.  high.  The  dry  gallon  contains  268.8 
cu.  in.,  being  \  bu. 

For  approximations,  the  bushel  may  be  taken  at  If  cu.  ft.; 
or  a  cubic  foot  may  be  considered  £  of  a  bushel. 

The  British  bushel  contains  2,218.19  cu.  in.  =  1.2837  cu.  ft. 
■=  1.032  U.  S.  bushels. 


LIQUID  MEASURE. 

4  gills  (gi.)  .  =  1  pint . pt. 

2  pints  . . .....  =  1  quart  . qt, 

4  quarts .  =  1  gallon  . gal. 

31  i  gallons  .  =  1  barrel  . bbl. 

.  2  barrels,  or  63  gallons  .  =  1  hogshead  . hhd. 

1  hhd.  =  2  bbl.  =  63  gal.  =  252  qt.  =  504  pt.  =  2,016  gi. 
The  U.  S.  gallon  contains  231  cu.  in.  =  .134  cu.  ft.,  nearly 
or  1  cu.  ft.  contains  7.480  gal.  The  following  cylinders  con¬ 
tain  the  given  measures  very  closely  : 


Diam. 

Height 

Diam. 

Height 

Gill . .  If  in. 

3  in. 

Gallon  .  7  in. 

6  in. 

Pint  .  3£in. 

3  in. 

8  gallons  14  in. 

12  in. 

Quart  .  3fin. 

6  in. 

10  gallons  14  in. 

15  in. 

With  water  at  its  maximum  density  (weighing  62.425  lb. 
per  cu.  ft.),  a  gallon  of  pure  water  weighs  8.345  lb. 

THE  METRIC  SYSTEM. 


25 


For  approximations,  1  cu.  ft.  of  water  is  considered  equal 
to  gal.,  and  1  gal.  as  weighing  8}  lb. 

The  British  imperial  gallon,  both  liquid  and  dry,  con¬ 
tains  277.274  cu.  in.  =  .16046  cu.  ft.,  and  is  equivalent  to  the 
volume  of  10  lb.  of  pure  water  at  62°  F.  To  reduce  U.  S.  to 
British  liquid  gallons,  divide  by  1.2.  Conversely,  to  convert 
British  into  U.  S.  liquid  gallons,  multiply  by  1.2;  or,  increase 
the  number  of  gallons  §. 


12  articles  = 
12  dozen  = 
12  gross  = 
2  articles  = 
20  articles  = 
24  sheets  = 
1  knot  (U 
1  meter 


MISCELLANEOUS  TABLE 

1 
1 


1 

1 

1 

1 

S.) 


20  quires  =  1  ream. 

1  league  =  3  miles. 

1  fathom  =  6  feet. 

1  hand  =  4  inches. 
1  palm  =  3  inches. 
1  span  =  9  inches. 
=  6,086.07  ft.  =  1|  miles  (roughly). 

—  3  feet  3f  inches  (nearly). 


dozen. 

gross. 

great  gross, 
pair, 
score, 
quire. 


THE  METRIC  SYSTEM. 

The  metric  system  is  based  on  the  meter,  which,  according 
to  the  U.  S.  Coast  and  Geodetic  Survey  Report  of  1884,  is  equal 
to  39.370432  inches.  The  value  commonly  used  is  39.37  inches, 
and  is  authorized  by  the  U.  S.  government.  The  meter  is 
defined  as  one  ten-millionth  the  distance  from  the  pole  to  the 
equator,  measured  on  a  meridian  passing  near  Paris. 

There  are  three  principal  units— the  meter,  the  liter  (pro¬ 
nounced  lee-ter),  and  the  gram,  the  units  of  length,  capacity, 
and  weight,  respectively.  Multiples  of  these  units  are  obtained 
by  prefixing  to  the  names  of  the  principal  units  the  Greek 
words  deca  (10),  hecto  (100),  and  kilo  (1,000);  the  submulti¬ 
ples,  or  divisions,  are  obtained  by  prefixing  the  Latin  words 
deci  (TV),  centi  (T^),  and  milli  (nsW)-  These  prefixes  form 
the  key  to  the  entire  system.  In  the  following  tables,  the 
abbreviations  of  the  princi  pal  units  of  these  submultiples  begin 
with  a  small  letter,  while  those  of  the  multiples  begin  with  a 
capital  letter ;  they  should  always  be  written  as  here  printed. 


26 


WEIGHTS  AND  MEASURES. 


MEASURES  OF  LENGTH. 


Name.  Meters.  U.  S.  In.  Feet. 

Millimeter  (mm.)  =  .001  =  .039370  =  .003281 

Centimeter  (cm.)  =  .010  =  .393704  =  .032809 

Decimeter  (dm.)  =  .100  =  3.937043  =  .328087 

Meter  (m.)  =  1.000  =  39.370432  =  3.280869 

Decameter  (Dm.)  =  10.000  =  32.808690 

Hectometer  (Hm.)  =  100.000  =  328.086900 

Kilometer  (Km.)  =  1,000.000  =  .621  mi.  =  3,280.869000 

Myriameter  (Mm.) 


6.214  mi.  =  32,808.690000 


=  100.000  = 

=  1,000.000  =  .621  mi.  = 

=  10,000.000 

The  centimeter,  meter,  and  kilometer  are  the  units  in 
practical  use,  and  may  he  said  to  occupy  the  same  position 
in  the  metric  system  as  do  inches,  yards,  and  miles  in  the 
U.  S.  and  English  system  of  measurement. 


MEASURES  OF  AREA. 

Name.  Sq.  Met.  Sq.  In.  Sq.  Ft.  Acres. 

Sq.  millimeter  (mm.2)  =  .0000010=. 001550 
Sq.  centimeter  (cm.2)  =  .0001 000=. 155003  ==.00107641 
Sq.  decimeter  (dm.2)  =  .0100000=15.5003  =.10764100 
Sq.  meter,  or  centare 

(in.2,  or  ca.)  =  1.000000=1,550.03=  10.764100 =.000247 
Sq.  decameter,  or  are 

(Dm.2,  or  A.)  =  100.0000=  155,003=1,076.4101=  .024710 

Hectare  =10,000.00  =107,641.01=  2.47110 

Sq.  kilometer  =  .3861099  sq.  mi.  =10,764,101=  247.110 

Sq.  myriameter  =  38.61090  sq.  mi.  =24,711.0 


MEASURES  OF  VOLUME. 

Name.  Cu.  Met.  Cu.  In.  Cu.  Ft.  Cu.  Yd. 

Cu.  centimeter  (cm.3)  =  .000001=  .061025 

Cu.  decimeter  (dm.3)  =  .001000=  61.0254 
Centistere  =  .010000  =  610.2540  =  .35316 

Decistere  =  .100000  =  3.53156 

Stere  [=  cu.m,  (m.3)]  =  1.000000  =  35.3156  =  1.308 

Decastere  =10.000000  =353.156  =13.080 


THE  METRIC  SYSTEM. 


27 


MEASURES  OF  CAPACITY. 

Name. 

Milliliter  (ml.)  | 

(=cu.  centimeter)  { 

Centiliter  (cl.) 

Deciliter  (dl.) 

Liter  (1.)  (=  cubic  ) 
decimeter)  j 
Decaliter  (Dl.)  ) 

(=  centistere)  J 
Hectoliter  (HI.)  ) 

(=  decistere)  j 
Kiloliter  (Kl.) 

(=  cu.  m.,  or  stere) 

Myrialiter  (Ml  )  =  = 

(=  decastere)  j 
The  milliliter  (or  cubic  centimeter)  and  the  liter  are  the 
units  most  commonly  used.  A  liter  of  pure  water  at  4°  C.,  or 
39.2°  F.,  weighs  1  kilogram. 


Liters. 

Liq.  Meas. 

Dry  Meas. 

=  .00100  = 

.008454  gill 

=  .001816  pint 

=  .01000  = 

.081537  gill 

=  .018162  pint 

=  .10000  = 

.845370  gill 

=  .18162  pint 

=  1.0000  = 

(  1.05671  qt. 

(  .264179  gal. 

=  .11351  peck 

=  10.000  = 

2.64179  gal. 

=  1.1351  peck 

=  100.00  = 

26.4179  gal. 

=  2.83783  bu. 

=  1,000.0  = 

264.179  gal. 

=  28.3783  bu. 

=  10,000  = 

2641.79  gal. 

=  283.783  bu. 

METRIC  WEIGHTS. 

The  gram  is  the  basis  of  metric  weights,  and  is  the  weight 
of  a  cubic  centimeter  of  distilled  water  at  its  maximum 
density,  at  sea  level,  Paris,  barometer  29.922  inches. 


Name . 

Milligram(mg.)= 
Centigram  ( eg. )  = 
Decigram  (dg.)  = 
Gram  (g.)  = 

Decagram  (Dg.)= 
Hectogr’m  (Hg)= 
Kilogram  (Kg.)  = 
My  riogr’  m  ( Mg ) = 
Quintal  (Q.)  = 


Grams.  Grains.  Av.  Oz 
.001=  .01543 
.010=  .15432 
.100=  1.54323 
1.000=15.43235= 

10.000  = 

100.000 
1,000.000 
10,000.000 
100,000.000 


Av.  Lb. 


.03527= 
=  .35274= 
=  3.52739= 
=35.27395= 


.0022046 
.0220462 
.2204622 
2.2046223 
=  22.0462234 

=  220.4622341 

Tonneau  (T.)  =1,000,000.000  =2,204.6223410 

The  gram  and  the  kilogram  (called  kilo )  are  the  units  in 
common  use. 


28 


WEIGHTS  AND  MEASURES. 


FACTORS  FOR  CONVERSION. 

For  approximations,  it  may  be  useful  to  remember  tne  ml- 
lowing  : 

1  centimeter  =  .4  in.  (nearly). 

1  meter  =  40  in.  (roughly). 

1  kilometer  ==  £  mile  (nearly). 

1  liter  =  1  liquid  quart  (nearly). 

1  liter  =  |  peck  (nearly). 

1  gram  =  15.4  grains. 

1  kilogram  =  2£  pounds. 

To  convert  metric  measures  into  U.  S.  measures ,  by  use  of 
the  preceding  tables,  find  the  desired  equivalent  in  U.  S. 
measure  of  a  metric  unit  of  the  denomination  given,  and 
multiply  this  equivalent  by  the  metric  number.  For  ex¬ 
ample,  it  is  desired  to  find  the  equivalent  in  pounds  of  19.6 
kilos.  From  the  table  of  weights,  1  kilo  =  2.2046  lb. ; 
hence,  19.6  kilos  =  2.2046  X  19.6  =  43.21  lb.  In  similar  man¬ 
ner,  8  liters  expressed  in  U.  S.  gallons  =  .264179X8  =  2.113432 
gal. 

To  convert  U.  S.  measures  into  metric  measures,  find  how 
much  a  metric  unit  of  the  desired  denomination  is  equal  to 
in  U.  S.  measure,  and  divide  the  given  number  by  this  equiv¬ 
alent.  For  example,  it  is  desired  to  convert  4^  miles  into 
kilometers.  From  the  table  of  lengths,  it  is  found  that  a 
kilometer  is  .621  mi. ;  hence,  dividing  4.5  by  .621,  the  result  is 
7.24  kilometers. 

Other  useful  conversion  factors  are  as  follows : 

Length.— 1  in.  =  .0254  meter;  1  ft.  =  .3048  meter;  1  yd. 
=  .9144  meter;  1  mi.  =  1,609.34  meters  =  1.609  kilometers. 

Area.— 1  sq.  in.  =  .000645  square  meter;  1  sq.  ft.  =  .0929 
square  meter ;  1  sq.  yd.  =  .836  square  meter ;  1  acre  =  4,047. 
square  meters. 

Capacity.— 1  cu.  in.  =  .0164  liter;  1  U.  S.  bushel  =  35.24 
liters;  1  U.  S.  dry  quart  =  1.101  liters;  1  U.  S.  peck  =  8.81 
liters;  1  cu.  yd.  =  765  liters;  1  U.  S.  liquid  quart  =  .9463 
liters ;  1  U.  S.  gallon  =  3.785  liters. 

Weight.— 1  grain  =  .0648  gram;  1  avoirdupois  ounce  = 
28.349  grams;  1  Troy  ounce  =  31.103  grams;  1  avoirdupois 
pound  =  453.59  grams. 


SPECIFIC  GRA  VITIES  AND  WEIGHTS. 


29 


SPECIFIC  GRAVITIES  AND  WEIGHTS. 

The  specific  gravity  of  a  solid  or  liquid  body  is  the  ratio 
between  its  weight  and  that  of  a  like  volume  of  distilled 
water.  If  the  solid  is  of  irregular  shape,  its  specific  gravity 
may  he  found  by  weighing  it  in  air  and  in  water ;  the  loss  of 
weight  in  water  is  the  weight  of  an  equal  volume  of  water ; 
hence,  if  This  the  weight  in  air,  and  W'  the  weight  in  water, 

W 

the  specific  gravity  is  •=== — 

iv —  w 

The  weight  of  water  in  various  conditions  is  as  follows : 

Water,  pure  at  32°  F.  weighs  62.417  lb.  per  cu.  ft. 

Water,  pure  at  39°  F.  weighs  62.425  lb.  per  cu.  ft 

Water,  pure  at  62°  F.  weighs  62.355  lb.  per  cu.  ft. 

Water,  pure  at  212°  F.  weighs  59.700  lb.  per  cu.  ft. 


Water,  sea . weighs  64.080  lb.  per  cu.  ft. 

Ice  . weighs  57.400  lb.  per  cu.  ft. 

Snow,  fresh . weighs  5  to  12  lb.  per  cu.  ft. 

Snow,  wet . weighs  15  to  50  lb.  per  cu.  ft. 


Metals. 


Name  of  Metal. 

Weight 
per  Cu.  In. 
Pounds. 

Weight 
per  Cu.  Ft. 
Pounds. 

Specific 

Gravity. 

Aluminufa . 

.096 

166 

2.66 

Antimony . 

.242 

418 

6.70 

Bismuth . 

.350 

607 

9.74 

Brass,  cast . 

.292 

504 

8.10 

Brass,  rolled . 

.303 

524 

8.40 

Bronze  (gun  metal)  . 

.305 

529 

8.50 

Copper,  cast . 

.314 

542 

8.70 

Copper,  rolled . 

Gold,  24  carat  . 

.321 

555 

8.90 

.694 

1,204 

19.26 

Iron,  cast  . 

.260 

450 

7.21 

Iron,  wrought . 

.277 

480 

7.66 

Lead,  commercial . 

.410 

710 

11.38 

Mercurv,  60°  F . 

.489 

846 

13.58 

Platinum  . 

.779 

1,342 

21.50 

Silver  . 

.378 

655 

10.50 

Steel . 

.283 

490 

7.85 

Tin,  cast . 

.265 

459 

7.35 

Zinc . . . 

.253 

437 

7.00 

c 


30 


WEIGHTS  AND  MEASURES. 


Building  Materials,  Etc. 


Name  of  Material. 

Weight 
per  Cu.  Ft. 
Pounds. 

Specific 

Gravity. 

Bluestone  . 

1G0 

2.56 

Brick,  pressed  . 

150 

2.40 

Brick,  common . 

125 

2.00 

Chalk  . 

156 

2.50 

Charcoal . 

15-30  ' 

.24-.48 

Clay,  compact  . 

119 

1.90 

Coke,  loose . . 

23-32 

•37-.51 

Coal,  hard,  solid  . 

93.5 

1.50 

Coal,  hard,  broken . 

54 

.865 

Coal,  soft,  solid . 

84 

1.35 

Coal,  soft,  broken . 

50 

.80 

Concrete,  cement  . 

140 

2.25 

Cement,  Portland  . 

80-100 

1.4( 

Cement,  Rosendale . 

56 

.89 

Earth,  dry,  shaken . 

82-92 

1.36 

Earth,  rammed . 

90-100 

1.52 

Earth,  moist,  shaken . 

75-100 

1.31 

Glass,  average  . 

186 

2.98 

Glass,  common  window  . 

;i57 

2.52 

Granite . . 

‘170 

2.72 

Gravel  (see  sand)  . 

Limestones  and  marbles . 

168 

2.70 

Lime,  quick  . 

53 

.85 

Marble  (see  limestone) . 

Plaster  of  Paris . 

141.6 

2.27 

Porphyry  . 

170.0 

2.73 

Quartz . . . 

165 

2.65 

Sand . 

90-106 

2.65 

Sandstone  . . 

151 

2.41 

Shales  . 

162 

2.60 

Slate  . 

175 

2.80 

Trap  rock  . 

187 

3.00 

Masonry. 

Common  brickwork,  cement  mortar 

130 

2.10 

Common  brickwork,  lime  mortar . 

120 

1.90 

Granite  or  limestone  rubble,  dry . 

138 

2.21 

Granite  or  limestone  rubble . 

154 

2.45 

Granite  or  limestone,  well  dressed 

165 

2.65 

Mortar,  hardened  . 

103 

1.65 

Pressed  brickwork . 

140 

'  2.25 

Sandstone  rubble  . 

145 

2.32 

FORMULAS. 


31 


Woods  (Dry). 


Name  of  Material. 

Weight 

per 

Foot. 

B.  M. 

Weight 

per 

Cu.  Ft. 
Pounds. 

Specific 

Gravity. 

Ash  . 

3.9 

47.0 

.752 

Ash,  American  white... 

3.2 

38.0 

.610 

Boxwood  . 

5.0 

60.0 

.960 

Cherry . 

3.5 

42.0 

.672 

Chestnut . 

3.4 

41.0 

.660 

Cork . 

1.3 

15.6 

.250- 

Elm . . 

2.9 

35.  Q 

.560 

Ebony . 

6.3 

76.1 

1.220 

Hemlock  . 

2.1 

25.0 

.400 

Hickory  . 

4.4 

53.0 

.850 

1  agnum  vitae  . 

6.9 

83.0 

1.330 

Mahogany,  Spanish . 

4.4 

53.0 

.850 

Mahogany,  Honduras  ... 

2.9 

35.0 

.560 

Maple . 

4.1 

49.0 

.790 

Oak,  live . 

4.9 

59.3 

.950 

Oak,  white . 

4.0 

48.0 

.770 

Oak.  red . 

3.3 

40.0 

.640 

Pine,  white  . . 

2.1 

25.0 

.400 

Pine,  yellmv . 

2.8 

34.3 

.550 

Pine,  Southern . 

3.7 

45.0 

.720 

Sycamore  . 

3.1 

37.0 

.590 

Spruce . 

2.1 

25.0 

.400 

Walnut  . 

3.2 

38.0 

.610 

FORMULAS. 


Formulas  are  simply  short  methods  of  indicating  opera¬ 
tions  otherwise  expressed  by  rules,  by  using  letters  and  signs 
in  place  of  words.  The  letters  are  usually  those  of  the 
English  alphabet,  and  the  signs  are  those  previously  given. 
Besides  showing  at  a  glance  the  various  steps,  formulas 
are  much  more  convenient  than  rules  to  memorize.  Many 
people  are  unnecessarily  deterred  from  using  a  formula, 
because  a  few  letters  are  used  instead  of  many  words ;  but  a 
formula  can  really  be  more  readily  followed  than  a  rule.  We 


32 


FORMULAS. 


shall  confine  our  attention  to  explanations  of  some  simple 
formulas,  and  to  showing  how  a  formula  may  be  transposed 
so  as  to  obtain  any  required  term. 

To  show  the  similarity  between  a  rule  and  a  formula,  let  it 
be  required  to  find  the  area  of  footing  necessary  to  sustain 
a  certain  load,  having  given  the  safe  load  per  square  foot. 
The  rule  is :  Divide  the  total  load  in  pounds  by  the  safe  load 
in  pounds  per  square  foot ;  the  quotient  is  the  required  area  in 
square  feet.  Not  much  space  can  be  saved  by  expressing  such 
a  simple  rule  in  a  formula,  but  the  operation  is  more  quickly 
comprehended.  Let  the  total  load  in  pounds  be  represented 
by’the  letter  P,  the  safe  load  per  square  foot  by  the  letter  S, 
and  the  required  area  by  the  letter  A.  Then  the  rule  is 

p 

expressed  by  the  formula  A  =  -- 

A  formula  is  used  by  substituting  for  the  letters  the  quan¬ 
tities  known  in  the  problem,  and  finding  the  unknown  by 
performing  the  indicated  operations.  Sometimes  the  formula 
as  written  does  not  give  the  desired  quantity  directly,  but 
must  be  rearranged  so  as  to  enable  it  to  be  found.  This  is 
done  by  simple  operations,  the  aim  being  to  obtain  the 
desired  qiiantity  by  itself  on  one  side  of  the  equality  sign. 
Thus,  in  the  above  formula,  suppose  it  is  desired  to  find  the 
value  of  P,  A  and  S  being  given.  By  multiplying  A  and 

p 

by  S  (such  operation  being  called  clearing  of  fractions) 

there  results  A  X  S  =  P,  in  which  the  desired  quantity  P  is 
by  itself  and  is  found  to  be  equal  to  the  product  of  A  and  S. 
The  formula  is  further  shortened  by  omitting  the  X  sign, 
and  writing  A  S  =  P.  When  two  or  more  letters  are  thus 
written,  it  means  that  they  are  to  be  multiplied  together.  In 
a  similar  manner,  S  may  be  obtained,  by  dividing  the  last 

found  formula  through  by  A ;  thus,  S  =  ~  • 

Example. — The  safe  bearing  power  of  a  soil  is  1,500  lb.  per 
sq.  ft.  What  area  of  footing  is  required  to  sustain  a  load 
of  30,000  lb.? 

Here  A  is  wanted,  and  P  and  S  are  given.  Hence,  A  *=  Pc, 


FORMULAS. 


36 


30,000 


=  20  sq.  ft.  Again,  suppose  it  was  desired  to  ascer- 


1,500 

tain  how  much  per  sq.  ft.  a  footing  20  ft.  in  area  carried,  the 
total  load,  30,000  lb.,  being  known.  Then,  A  and  P  are 


given  to  find  S ;  or  S  =  =  = 


30,000 

20 


1,500  lb. 


The  following  formula  shows  how  to  determine  the  safe 
load  that  a  stone  beam  or  liptel  will  carry,  if  uniformly  loaded: 

2  bdlA  =  w, 


in  which 


b  = 
d  = 
A 
f 

L  = 
W  = 


JL 

breadth  in  inches ; 
depth  in  inches ; 
number  from  a  table ; 
factor  of  safety; 
length  in  feet ; 

safe  distributed  load,  in  pounds. 
Suppose  any  other  quantity  than  W  is  wanted  ;  it  may  be 
found  by  transposing  the  formula  ;  thus,  if  the  depth  to  sustain 
a  certain  load  is  required,  the  formula  is  thus  arranged : 
Multiplying  through  by  / L, 

2  b  d2  A  =  WfL. 

Arranging  so  as  to  have  d2  alone  on  one  side  of  the  =  sign, 

WfL 
2b  A 

Extracting  the  square  root, 

d 


d2  - 


\  2b A 


Example.— It  is  desired  to  carry  a  distributed  load  of 
3,840  lb.  on  a  piece  of  bluestone  flagging  4  ft.  wide  and  6  ft. 
span,  using  a  factor  of  safety  of  10.  How  thick  must  the  stone 
beam  be?  Here,  W  =  3,840  lb. ;  5  =  4  ft.  X  12  =  48  in. ;  L 
=  6  ft. ;  /  =  10  ;  A  is  found  from  a  table  to  be  150  for  blue- 
stone  ;  then  d  is  the  required  term.  Substituting  the  values, 
there  results 


d 


3,840  X  10  X  6 


=  V  16  =  4  i 


in. 


2  X  48  X  150 

A  rule  for  finding  the  strength  of  a  wooden  column  is  •. 
From  the  ultimate  compressive  strength  of  the  material  in  pounds 
per  square  inch,  subtract  the  fraction :  the  ultimate  strength 


34 


FORMULAS. 


multiplied  by  the  length  of  column  in  inches ,  and  divided  by  100 
times  the  least  side  in  inches.  The  difference  is  the  ultimate 
strength  of  the  column  in  pounds  per  square  inch.  This  rule  is 
rendered  much  more  intelligible  by  using  a  formula  ;  thus : 

Let  S  =  ultimate  strength  of  column  in  lb.  per  sq.  in. ; 

ultimate  compressive  strength  of  material  in 
lb.  per  sq.  in.  ; 

length  of  column,  in  inches ; 
least  side  of  column,  in  inches. 

Ul 


U 

l  = 
d 


Then, 


S  =  U- 


100  d' 

The  values  of  U  for  different  woods  are  found  in  tables. 

Example.— The  ultimate  compressive  stress  of  white  pine, 
parallel  to  the  grain,  is  8,500  lb.  per  sq.  in.  What  is  the  ulti¬ 
mate  load  a  10"  X  10"  column  20  ft.  long  will  carry? 

Looking  through  the  problem,  it  is  found  that  all  the  quan¬ 
tities  in  the  formula  are  given  except  S' ;  the  length  expressed 
in  inches  =  240  in. ;  and  the  least  side  is  10  in.,  as  the  col¬ 
umn  is  square.  Substituting  these  values  in  the  formula 

Ul 


S  =  3,500  - 


S 

3,500  X  240 


U  — 


100  d’ 


=  3,500  —  840  =  2,660  lb. 


100  x  10 

Suppose  it  is  desired  to  find  the  side  of  a  square  wooden 
column  to  carry  a  known  load.  The  preceding  formula  con¬ 
tains  the  required  term  d,  but  as  it  also  involves  S,  which 
depends  on  d,  that  term  must  be  eliminated.  Let  P  represent 
the  total  load  on  the  column ;  then,  since  the  sectional  area 
is  dA,  P  =  d-  S ;  or,  substituting  for  £  its  value, 


Ul  ' 
100  d. 


d2  U- 


p  =  at  ^  u- 

Multiplying  by  100  and  dividing  by  U, 

dl. 


d  U  l 
100  * 


,0°4  =  ,oo  d* 


V 

Such  a  quantity  must  be  added  to  both  sides  of  this  equa¬ 
tion  (so  as  not  to  change  its  value)  as  will  make  the  right  side 

l- 

a  perfect  square.  This  quantity  is  found  by  trial  to  be 


Then, 


100 


r- 


-*  + 

U  ^  400 


100  d*-dl  +  ^  or 


400' 


LINES  AND  PLANE  SURFACES. 


35 


Extracting  the  square  root  of  both  members,  placing  : 


20 


on  the  left  of  the  equality  sign,  and  dividing  by  10, 

l 


l 


=  d. 


/loop  P  1A  ,  l  ,1  ;100P  ,  P 

\  U  +  400  0  20  ’  and  lo\  u  +  400  1  200 

=  y  xb<s >  multiplying  the  expression  under  the  radical 


by  it, 


*\u 


l 


!P  P 

-  -a - - =  d* 

r  T  40,000  ^  200 


In  using  any  formula ,  care  must  be  taken  to  have  all  dimen¬ 
sions weights ,  etc.  expressed  in  the  units  required  by  the  for  mula. 


MENSURATION. 


LINES  AND  PLANE  SURFACES. 

TRIANGLE. 

Right  Triangle. 

Hypotenuse  c  =  ]/  a2  +  b-. 
Side  a  =  | /c2  —  b2. 

Side  b  =  ]/ c2  —  a2. 
Area  —  i  a  b. 

Oblique  Triangle. 

If  altitude  or  height  h  and  base 
known  : 

Area  =’  |  b  li. 

If  the  three  sides  are  known  : 

Let  s  =  £(a  +  b  +  c). 

Area  =  i/  s(s  —  a)(s  —  b){s  —  c). 


*This  formula,  while  given  as  an  exercise  in  formulas,  is 
also  useful  in  calculating  directly  the  size  of  a  square  wooden 
column,  instead  of  ascertaining  it  by  trial,  as  is  usual. 


36 


MENSURATION. 


TRAPEZIUM. 

Divide  into  two  triangles  and  a  trapezoid. 

Area  =  £b  h'+  $a(h'+  h)+  %ch ; 
or,  area  =  h[bh'+ch-\-a(h'+h)]. 


REGULAR  POLYGONS. 

Divide  the  polygon  into  equal  triangles  and  find  the  sum  of 
the  partial  areas.  Otherwise,  square  the  length  of  one  side 
and  multiply  by  proper  number  from  the  following  table: 


Name. 

No.  Sides. 

Multiplier. 

Triangle 

3 

.433 

Square 

4 

1.000 

Pentagon 

5 

1.720 

Hexagon 

6 

2.598 

Heptagon 

7 

3.634 

Octagon 

8 

4.828 

Nonagon 

9 

6.182 

Decagon 

10 

7.694 

IRREGULAR  AREAS. 

Divide  the  area  into  trapezoids,  triangles,  parts 
of  circles,  etc.,  and  find  the  sum  of  the  partial 
areas. 

If  the  figure  is  very  irregular,  the  approximate 
area  may  be  found  as  follows :  Divide  the  figure 
into  trapezoids  by  equidistant  parallel  lines  b,  c ,  d, 
etc.  The  lengths  of  these  lines  being  measured, 
then,  calling  a  the  first  and  n  the  last  length,  and 


y  the  width  of  strips, 

Area  =  +  &  +  c  -f  etc.  +  m^. 


LINES  AND  PLANE  SURFACES. 


37 


CIRCLE. 

A  =  area. 

7 r  {pi)  =  3.1416. 

Z  -  .7854. 

4 

p  =  perimeter  or  circumference. 
p  =  n  cl  =  3.1416  d. 
p  =  tyd  (approximately). 
p  —  2  7r  r  =  6.2832  r. 

77  3.1416 

d  —  275p  (approximately). 
d  =  1.128]/ A. 

r  -Jt- 

2  77  6.2832' 

r  =  .5642j/  A. 

A  —  ~~  =  .7854  d1. 

4 

A  «=  77  r2  =  3.1416 1*. 

Side  of  square  of  area  equal  to  circle  =  .8862  d. 

Diameter  of  circle  of  area  equal  to  a  given  square  =  1.128 
X  side. 


RING. 

Area  =  .7854(D2  -  d2). 


SECTOR. 

If  radius  r  and  rise  h  are  known,  chord  c 
=  2]/2hr  —  h2. 

If  chord  c  and  rise  h  are  known, 

c2  +  4  /i2 
radius  r  =  • 

c2 

Approximately,  r  = 


Subchord  e  =  ^i/c2  +  4/t2. 


38 


MENSURATION. 


g  g _ c 

If  h  is  not  more  than  .4  c,  length  of  arc  l  —  — - — ,  nearly. 

O 

If  l  and  r  are  known, 

Angle  E*  =  57.296 ^ 

=  57. 3p  nearly. 

Area  =  ilr. 

If  r  and  angle  E*  are  known, 

Iengtli  (  =  ^  =  E,  nearly. 

■-=  ,0175  Er. 

Area  =  .0087  r2  E. 

SEGM  ENT. 


- 


Area  of  segment  =  area  of  sector  —  area 
of  triangle. 
xV  Height  of  triangle  =  r  —  h. 

If  l,  r,  c,  and  h  are  known, 

Area  =  ilr  —  ic  (r  —  h). 

If  c,  h,  r,  and  E  are  known,  find  l  as  shown 
under  Sector;  the  area  may  then  be  found 


by  the  preceding  formula. 


ELLI  PSE. 


t  V 


7T-*  lD2  +  &  {D-d)* 

\  2  8.8  ’ 
Area  =  .7854  I)  d. 


*  If  the  angle  E  contains  minutes  and  seconds,  these  must 
be  expressed  in  decimals  of  a  degree.  Divide  the  minutes  by 
60,  and  the  seconds  (if  any)  by  3,600,  and  add  the  sum  of  the 
decimals  to  the  degrees;  thus,  30° 45' 36"  =  30°  +  U  + 

=  30.76°.  If  E  is  given  in  degrees  and  decimals,  it  may  be 
reduced  to  minutes  and  seconds  thus,  .76°  =  .76°  X  60'  —  45.6'; 
.6'  x  60"  =  36" ;  hence,  30.76°  =  30°  45'  36". 

t  The  perimeter  of  an  ellipse  cannot  be  exactly  determined, 
and  this  formula  is  merely  an  approximation 'giving  fairly 
close  results. 


SOLIDS  AND  CURVED  SURFACES. 


39 


H  ELIX. 

d  —  diameter  of  helix  ; 
l  =  length  of  1  turn  of  helix  ; 
t  =  pitch,  or  rise  in  1  turn  ; 
n  =  number  of  turns ; 
it2  =  9.8696. 

I  =  j/^d^M2. 
t  =  V  F  —  vSd*. 

Total  length  =  nl  =  n\/  F1  d'2  -f  t-. 


SOLIDS  AND  CURVED  SURFACES. 

C  —  convex  surface  ; 

S  —  whole  surface ; 

—  C  +  area  of  end  or  ends ; 

A  =  area  larger  base  or  end  ; 
a  =  area  smaller  base  or  end ; 

P  =  perimeter  of  larger  base  ; 
p  —  perimeter  qf  smaller  base ; 

D  =  larger  diameter  ; 
d  —  smaller  diameter ; 

V  =  volume  of  solid. 

In  a  cylinder  or  prism, 

A  =  a,  P  =  p,  and  D  —  d. 


CYLINDER. 

c  =  Ph  =  3.1416  d  h ; 

S  =  3.1416  d  h  +  1.5708  d- ; 
V  =  Ah  =  .7854  d-  h. 


FRUSTUM  OF  CYLINDER. 


h  =  i  sum  of  greatest  and  least  heights ; 

C  =  Ph  =  3.1416  d  h; 

S  —  3.1416  dli  +  .7854  d-  +  area  of  elliptical 
top; 

V  =  A  h  =  .78M  d2  h. 


40 


MENSURATION. 


PRISM  OR  PARALLELOPIPED. 

C  =  Eh] 

S  = Eh +2 A; 

V  =  Ah. 

For  prisms  with  regular  polygon  as 
bases,  F  =  length  of  one  side  X  number  of  sides. 

To  obtain  area  of  base,  if  it  is  a  polygon,  divide  it  into  tri¬ 
angles,  and  find  sum  of  partial  areas. 


FRUSTUM  OF  PRISM. 

If  a  section  perpendicular  to  the  edges  is  a 
triangle,  square,  parallelogram,  or  regular  polygon, 
sum  of  lengths  of  edges 


V  = 
tion. 


number  of  edges 


Xarea  of  right  sec- 


CON  E. 

c  c=  ipz  =  1.5708  d  l ; 

S  =  1.5708  dl  +  . 7854 d2 * * S 6 * 8; 

V  =  ~  =  .2618  d2  h. 

6 


FRUSTUM  OF  CONE. 

c  a  iZ(P  +  p)=  1.5708  l(D  +  d); 

S  =  1.5708 1  (D  +  d)  +  .7854  (D°-  +  cZ2); 
V  =  .2618 h  (D2  +  Dd  +  (E). 


PYRAM  ID. 


C  =  hPl] 

S  =  ±El  +  A; 


V  = 


Ah 

8  ' 


To  obtain  area  of  base,  divide  it  into  tri¬ 
angles,  and  find  their  sum. 


SOLIDS  AND  CURVED  SURFACES. 


41 


FRUSTUM  OF  PYRAMID. 

C  =  U(P  +  p)i 
S  =  5 1  (P  +  p)  A  A  +  Q>  j 

V  =  |  h  (  A  +  a  +  -]/  A  a). 


PRISMOID. 

A  prismoid  is  a  solid  having  two  parallel  plane  ends,  the 
edges  of  which  are  connected  hy  plane  triangular  or  quadri¬ 
lateral  surfaces. 

A  =  area  one  end  ; 
a  =  area  of  other  end  ; 
m  —  areaof  section  midway  between  ends; 
l  —  perpendicular  distance  between  ends; 

V  =  ^(4  +  a  +  4m). 

The  area  m  is  not  in  general  a  mean  between  the  areas  of 
the  two  ends,  hut  its  sides  are  means  between  the  correspond¬ 
ing  lengths  of  the  ends.  ^  ^ 

Approximately,  V  =  — ~ —  l. 


42 


MENSURATION. 


CALCULATING  THE  WEIGHT  OF  CASTINGS,  ETC. 

The  first  step  is  to  ascertain  the  number  of  cubic  inches  in 
the  casting.  To  illustrate  the  method,  consider  the  column 
shown  in  the  figure  to  be  divided  into  several  parts,  as  given 

below.  With  irregular  shapes,  as 
at  e,  follow  the  principle  of  “give 
and  take,”  reducing  the  shape  to 
an  equivalent  one,  easy  to  calcu¬ 
late.  The  operations  are  then  as 
follows : 

Cu.  In. 

Cylinder  a,  excluding 
cap.  Net  height  =  12  ft. 

—  (14  in.  +  1  in.)  =  141.5 
in.;  net  area  =  10”  circle 

—  84”  circle  =  21.8  sq.  in. 

Contents  ==  21.8  sq.  in.  X 
141.5  in.  =  3,084.7 

Base  b  —  19  in.  X  19  in. 

X  14  iu.  =  541.5  cu.  in.; 
deduct  area  of  10”  circle 
X  Is”  —  H7.8  cu.  in.;  also, 
for  corners  (5”  square — 5” 
circle)  X  14”  —  8.1  cu.  in. 

Net  contents 


Triangular  ribs  c  =  4  (44  in.  X  7  in.)  X  14  in.  X  4  = 
Brackets  d.  Horizontal  part  d  is,  very  nearly,  5  in. 
X  5  in.  X  14  in.  =  374  cu.  in.  Vertical  part  e :  To-com- 
pensate  for  swelled  portion  next  cylinder  (see  e'),  con¬ 
sider  vertical  portion  as  triangular,  with  sides  5  in. 
X  7  in.;  its  contents  are  4  (5  in.  X  7  in.)  X  14 in.  —  19.7 
cu.  in.  Each  bracket  —  57.2  cu.  in.;  4  brackets  =  57.2 
X  4  » 

Lugs  f  —  11  in.  X  5  in.  X  1  in.  =  55  cu.  in.;  deduct 
4  (4”  square  —  4”  circle)  X  1”  =  1.7  cu.  in.;  also,  two 
f”  holes  —  .9  cu.  in.  Net  contents  of  each  lug,  52.4 
cu.  in.;  4  lugs  =  52.4  X  4  = 

Cap  g  —  (16”  X  16”  —  4”  circle)  X  14”  = 


415.6 

70.9 


228.8 


209.6 

365.2 


Carried  forward 


4,374.8 


SOLIDS  AND  CUE  VED  SURFACES. 


43 


Brought  forward,  '  4,374.8 

Upper  part  of  cap  li  =  (16"  square  —  12"  square) 

X  1"  thick  —  deduction  for  bevel ;  256  cu.  in.  —  144 
cu.  in.  =  112  cu.  in.  Portion  to  he  deducted  consists 
of  4  wedges,  each  16  in.  X  1  in.  at  the  back,  13  in.  at 
the  edge,  which  is  1|  in.  from  back;  by  rule  for  wedges, 
deduction  is  [J  X  (16  in.  +  16  in.  -f  13  in.)  X  1  in. 

X  li  in.]  X  4  =  45  cu.  in.  Net  contents  of  part  li  — 

112  —  45  =  67.0 

Total  contents  of  column  =  4,441.8 

One  cu.  ft.  of  cast  iron  weighs  450  lb.,  or  1  cu.  in.  weighs 
.26  lb. — called  i  lb.,  roughly.  Hence  the  weight  is  4,442  X  >26 
=  1,155  lb.  This  calculation  is  much  more  detailed  than  is 
usual ;  generally,  no  account  is  taken  of  rounded  corners, 
small  fillets,  holes,  etc. 

When  a  casting  or  a  rolled  shape  of  steel,  etc.  is  of  uniform 
cross-section  throughout— as  a  rail,  I  beam,  or  channel— the 
weight  may  be  very  expeditiously  determined  after  calcu¬ 
lating  the  sectional  area.  A  cubic  foot  of  wrought  iron 
weighs  480  lb.;  hence,  a  piece  1  yd.  long  and  1  in.  square 
contains  36  cu.  in.,  and  weighs  of  480  lb.  =  10  lb.;  or,  if 
1  ft.  long  and  1  in.  square,  weighs  ^  =  3^  lb.  Therefore,  if 
the  sectional  area  be  known  or  calculated,  the  weight  per 
foot  may  be  found  by  taking  the  area,  or  by  multiplying 
the  latter  by  3£.  This  result  will  be  in  pounds,  and,  if  multi¬ 
plied  by  the  total  length  in  feet  of  the  member,  will  give  the 
whole  weight. 

If  the  member  is  made  of  steel,  which  weighs  490  lb.  per 
cu.  ft.,  the  weight  per  foot  may  be  determined  by  multiplying 
the  sectional  area  by  3.4.  For  cast  iron  the  multiplier  is  3j. 

Example.— What  is  the  weight  per  foot  of  a  20"  steel  I 
beam,  having  a  sectional  area  of  26.4  sq.  in.?  26.4  X  3.4  =  89.76 
lb.,  or,  practically,  90  lb.  By  reference  to  Table  XIX,  page 90, 
it  will  be  seen  that  this  is  the  weight  given. 

If  the  weight  per  foot  is  given,  and  it  is  desired  to  find  the 
sectional  area,  the  former,  divided  by  or  multiplied  by  .3. 
will  give  the  required  area.  For  steel,  the  multiplier  is 
.294,  and  for  cast  iron  .32. 


44 


MENSURATION. 


CIRCUMFERENCES  AND  AREAS  OF 
CIRCLES  FROM  1-64  TO  100. 


Diam. 

Circum. 

Area. 

ISt 

.0491 

.0002 

3*2 

.0982 

.0008 

1 

T5 

.1963 

.0031 

.3927 

.0123 

3 

.5890 

.0276 

l 

.7854 

.0491 

5 

TS 

.9817 

.0767 

JL 

1.1781 

.1104 

7 

T5 

1.3744 

.1503 

i 

5 

1.5708 

.1963 

9 

T5 

1.7671 

.2485 

1 

1.9635 

.3068 

H 

2.1598 

.3712 

1 

2.3562 

.4418 

13 

T5 

2.5525 

.5185 

7 

8 

2.7489 

.6013 

1  5 

T5 

2.9452 

.6903 

l 

3.1416 

.7854 

n 

3.5343 

.9940 

H 

3.9270 

1.2272 

u 

4.3197 

1.4849 

H 

4.7124 

1.7671 

11 

5.1051 

2.0739 

If 

5.4978 

2.4053 

H 

5.8905 

2.7612 

2 

6.2832 

3.1416 

2| 

6.6759 

3.5466 

2f 

7.0686 

3.9761 

2f 

7.4613 

4.4301 

2| 

7.8.540 

4.9087 

2| 

8.2467 

5.4119 

2f 

8.6394 

5.9396 

2f 

9.0321 

6.4918 

3 

9.4248 

7.0686 

3| 

9.8175 

7.6699 

3f 

10.2102 

8.2958 

31 

10.6029 

8.9462 

31 

10.9956 

9.6211 

31 

11.3883 

10.3206 

3f 

11.7810 

11.0447 

31 

12.1737 

11.7933 

4 

12.5664 

12.5664 

4t 

12.9591 

13.3641 

4i 

13.3518 

14.1863 

Diam. 

Circum. 

Area. 

4| 

13.7445 

15.0330 

AX 

14.1372 

15.9043 

4f 

14.5299 

16.8002 

4f 

14.9226 

17.7206 

15.3153 

18.6555 

5 

15.7080 

19.6350 

6* 

5f 

16.1007 

20.6290 

16.4934 

21.6476 

5* 

16.8861 

22.6907 

5i 

17.2788 

23.7583 

51 

17.6715 

24.8505 

5f 

18.0642 

25.9673 

18.4569 

27.1086 

6 

18.8496 

28.2744 

19.2423 

29.4648 

6y 

19.6350 

30.6797 

6f 

20.0277 

31.9191 

6i 

20.4204 

33.1831 

6| 

20.8131 

34.4717 

Of 

21.2058 

35.7848 

21.5985 

37.1224 

7 

21.9912 

38.4846 

7i 

h 

7| 

22.3839 

39.8713 

22.7766 

41.2826 

23.1693 

42.7184 

7£ 

23.5620 

44.1787 

7* 

23.9547 

45.6636 

7f 

24.3474 

47.1731 

7f 

24.7401 

48.7071 

8 

25.1328 

50.2656 

81- 

25.5255 

51.8487 

8| 

25.9182 

53.4563 

8f 

26.3109 

55.0884 

8^ 

26.7036 

56.7451 

8f 

27.0963 

58.4264 

8f 

27.4890 

60  1322 

81 

27.8817 

61.8625 

9 

28.27-44 

63.6174 

9t 

28.6671 

65.3968 

29.0598 

67.2008 

9f 

29.4525 

69.0293 

9i 

29.8452 

70.8823 

9| 

30.2379 

72.7599 

9f 

30.6306 

74.6621 

TABLE  OF  CIRCLES. 


45 


Table — ( Continued) . 


Diam. 

Circum. 

Area. 

% 

31.0233 

76.589 

10 

31.4160 

78.540 

10} 

31.8087 

80.516 

lol 

32.2014 

82.516 

lot 

32.5941 

84.541 

10} 

32.9868 

86.590 

lot 

33.3795 

88.664 

lot 

33.7722 

90.763 

lot 

34.1649 

92.886 

11 

34.5576 

95.033 

Ilf 

34.9503 

97.205 

111 

35.3430 

99.402 

lit 

35.7357 

101.623 

111 

36.1284 

103.869 

lit 

36.5211 

106.139 

lit 

36.9138 

108.434 

lit 

37.3065 

110.754 

12 

37.6992 

113.098 

12* 

38.0919 

115.466 

12| 

38.4846 

117.859 

12f 

38.8773 

120.277 

12} 

39.2700 

122.719 

12* 

39.6627 

125.185 

12t 

40.0554 

127.677 

12* 

40.4481 

130.192 

13 

40.8408 

132.733 

13} 

41.2335 

135.297 

13} 

41.6262 

137.887 

13| 

42.0189 

140.501 

13} 

42.4116 

143.139 

13| 

42.8043 

145.802 

13t 

43.1970 

148.490 

13} 

43.5897 

151.202 

14 

43.9824 

153.938 

14} 

44.3751 

156.700 

14} 

44.7678 

159.485 

14* 

45.1605 

162.296 

14} 

45.5532 

165.130 

14| 

45.9459 

167.990 

14t 

46.3386 

170.874 

14} 

46.7313 

173.782 

15 

47.1240 

176.715 

15} 

47.5167 

179.673 

15} 

47.9094 

182.655 

16* 

48.3021 

185.661 

15} 

48.6948 

188.692 

D 


Diam. 

Circum. 

Area. 

15* 

49.0875 

191.748 

15t 

49.4802 

194.828 

15} 

49.8729  1 

197.933 

16 

50.2656 

201.062 

16} 

50.6583 

204.216 

16} 

51.0510 

207.395 

16* 

51.4437 

210.598 

16} 

51.8364 

213.825 

16* 

52.2291 

217.077 

16t 

52.6218 

220.354 

16} 

53.0145 

223.655 

17 

53.4072 

226.981 

17} 

53.7999 

230.331 

17} 

54.1926 

233.706 

17* 

54.5853 

237.105 

17} 

54.9780 

240.529 

17* 

55.3707  , 

243.977 

17* 

55.7634 

247.450 

17} 

56.1561 

250.948 

18 

56.5488 

254.470 

18} 

56.9415 

258.016 

18} 

57.3342 

261.587 

18* 

57.7269 

265.183 

18} 

58.1196 

268.803 

18* 

58.5123 

272.448 

18* 

58.9050 

276.117 

18} 

59.2977 

279.811 

19 

59.6904 

283.529 

19} 

60.0831 

287.272 

19t 

60.4758 

291.040 

19* 

60.8685 

294.832 

19} 

61.2612 

298.648 

19* 

61.6539 

302.489 

19* 

62.0466 

306.355 

19} 

62.4393 

310.245 

20 

62.8320 

314.160 

20} 

63.2247 

318.099 

20} 

63.6174 

322.063 

20* 

64.0101 

326.051 

20} 

64.4028 

330.064 

20* 

64.7955 

334.102 

20* 

65.1882 

338.164 

20} 

65.5809 

342.250 

21 

65.9736 

346.361 

21} 

66.3663 

350.497 

21} 

66.7590 

354.657 

46 


MENSURATION. 


Table — ( Continued). 


Diam. 

Circura. 

Area. 

21 1 

67.1517 

358.842 

21} 

67.5444 

363.051 

21} 

67.9371 

367.285 

21} 

68.3298 

371.543 

21} 

68.7225 

375.826 

22 

69.1152 

380.134 

221 

69.5079 

384.466 

22} 

69.9006 

388.822 

221 

70.2933 

393.203 

22} 

70.6860 

397.609 

22} 

71.0787 

402.038 

22} 

71.4714 

406.494 

221- 

71.8641 

410.973 

23 

72.2568 

415.477 

23} 

72.6495 

420.004 

23} 

73.0422 

424.558 

231 

73.4349 

429.135 

231 

73.8276 

433.737 

231 

74.2203 

438.364 

23} 

74.6130 

443.015 

231 

75.0057 

447.690 

24 

75.3984 

452.390 

241 

75.7911 

457.115 

24} 

76.1838 

461.864 

241 

76.5765 

466.638 

24} 

76.9692 

471.436 

24} 

77.3619 

476.259 

24} 

77.7546 

481.107 

24  } 

78.1473 

485.979 

25 

78.5400 

490.875 

25} 

78.9327 

495.796 

25} 

79.3254 

500.742 

251 

79.7181 

505.712 

25} 

80.1108 

510.706 

25} 

80.5035 

515.726 

25} 

80.8962 

520.769 

25} 

81.2889 

525.838 

26 

81.6816 

530.930 

26} 

82.0743 

536.048 

26} 

82.4670 

541.190 

26} 

82.8597 

546.356 

26} 

83.2524 

551. §47 

26} 

83.6451 

556.763 

26} 

84.0378 

562.003 

26} 

84.4305 

567.267 

27 

8-1.8232 

572.557 

Diam. 

Circum. 

Area. 

27} 

85.2159 

577.870 

27} 

85.6086 

583.209 

27} 

86.0013 

588.571 

27} 

86.3940 

593.959 

27} 

86.7867 

599.371 

27} 

87.1794 

604.807 

27} 

87.5721 

610.268 

28 

87.9648 

615.754 

28} 

88.3575 

621.264 

28} 

88.7502 

626.798 

28} 

89.1429 

632.357 

28} 

89.5356 

637.941 

28} 

89.9283 

643.549 

28} 

90.3210 

649.182 

28} 

90.7137 

654.840 

29 

91.1064 

660.521 

29} 

91.4991 

666.228 

29} 

91.8918 

671.959 

29} 

92.2845 

677.714 

29} 

92.6772 

683.494 

29} 

93.0699 

689.299 

29} 

93.4626 

695.128 

29} 

93.8553 

700.982 

30 

94.2480 

706.860 

30} 

94.6407 

712.763 

30} 

95.0334 

718.690 

30} 

95.4261 

724.642 

30} 

95.8188 

730.618 

30} 

96.2115 

736.619 

30} 

96.6042 

742.645 

30} 

96.9969 

748.695 

31 

97.3896 

754.769 

3H 

97.7823 

760.869 

31 1 

98.1750 

766.992 

31} 

98.5677 

773.140 

31} 

98.9604 

779.313 

31} 

99.3531 

785.510 

31} 

99.7458 

791.732 

31} 

100.1385 

797.979 

32 

100.5312 

804.250 

32} 

100.9239 

810.545 

32y 

101.3166 

816.865 

32} 

101.7093 

823.210 

32} 

102.1020 

829.579 

32} 

102.4947 

835.972 

32} 

102.8874 

842.391 

\ 


TABLE  OF  CIRCLES. 


47 


Table — ( Continued). 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

32f 

103.280 

848.833 

38* 

121.344 

33 

103.673 

855.301 

38* 

121.737 

331 

104.065 

861.792 

38} 

122.130 

331 

104.458 

868.309 

39 

122.522 

33f 

104.851 

874.850 

39} 

122.915 

331 

105.244 

881.415 

39} 

123.308 

33| 

105.636 

888.005 

39* 

123.700 

33* 

106.029 

894.620 

39} 

124.093 

331 

106.422 

901.259 

39} 

124.486 

34 

106.814 

907.922 

39* 

124.879 

341 

107.207 

914.611 

39} 

125.271 

341 

107.600 

921.323 

40 

125.664 

34f 

107.992 

928.061 

40} 

126.057 

341 

108.385 

934.822 

40} 

126.449 

341 

108.778 

941.609 

40* 

126.842 

341 

109.171 

948.420 

40} 

127.235 

341 

109.563 

955.255 

40* 

127.627 

35 

109.956 

962.115 

40* 

128.020 

351 

110.349 

969.000 

40} 

128.413 

351 

110.741 

975.909 

41 

128.806 

35f 

111.134 

982.842 

41} 

129.198 

351 

111.527 

989.800 

41} 

129.591 

351 

111.919 

996.783 

41* 

129.984 

351 

112.312 

1,003.790 

41} 

130.376 

351 

112.705 

1,010.822 

41* 

130.769 

36 

113.098 

1,017.878 

41* 

131.162 

361 

113.490 

1,024.960 

41} 

131.554 

361 

113.883 

1,032.065 

42 

131.947 

36f 

114.276 

1,039.195 

42} 

132.340 

361 

114.668 

1,046.349 

42} 

132.733 

361 

115.061 

1,053.528 

42* 

133.125 

361 

115.454 

1,060.732 

42} 

133.518 

361 

115.846 

1,067.960 

42* 

133.911 

37 

116.239 

1,075.213 

42* 

134.303 

371 

116.632 

1,082.490 

42} 

134.696 

371 

117.025 

1,089.792 

43 

135.089 

371 

117.417 

1,097.118 

43} 

135.481 

371 

117.810 

1,104.469 

43} 

135.874 

37f 

118.203 

1,111.844 

43* 

136.267 

371 

118.595 

1,119.244 

43} 

136.660 

371 

118.988 

1,126.669 

43* 

137.052 

38 

119.381 

1,134.118 

43* 

137.445 

381 

119.773 

1,141.591 

43} 

137.838 

381 

120.166 

1,149.089 

44 

138.230 

381 

120.559 

1.156.612 

44} 

138.623 

381 

120.952 

1,164.159 

44} 

139.016 

Area. 


1,171.731 

1,179.327 

1,186.948 

1,194.593 

1,202.263 

1,209.958 

1,217.677 

1,225.420 

1,233.188 

1,240.981 

1.248.798 

1 .256.640 
1,264.510 
1,272.400 
1,280.310 
1,288.250 

1.296.220 

1.304.210 

1.312.220 
1,320.260 
1,328.320 
1,336.410 
1,344.520 

1.352.660 
1,360.820 
1,369.000 

1.377.210 
1,385.450 
1,393.700 

1.401.990 

1.410.300 
1,418.630 

1.426.990 
1,435.370 
1,443.770 
1,452.200 

1.460.660 
1,469.140 

1.477.640 
1,486.170 
1,494.730 

1.503.300 
1,511.910 
1,520.530 
1,529.190 
1,537.860 


48 


MENSURATION. 


Table — ( Continued ) . 


Diam. 

Circuru. 

Area. 

Diam. 

Circum. 

44f 

139.408 

1,546.56 

50* 

157.473 

44* 

139.801 

1,555.29 

50* 

157.865 

441 

140.194 

1,564.04 

50* 

158.258 

44* 

140.587 

1,572.81 

50* 

158.651 

44* 

140.979 

1,581.61 

50| 

159.043 

45 

141.372 

1,590.43 

50* 

159.436 

451 

141.765 

1,599.28 

50* 

159.829 

45| 

142.157 

1,608.16 

51 

160.222 

45* 

142.550 

1,617.05 

51* 

160.614 

45| 

142.943 

1,625.97 

51* 

161.007 

45| 

143.335 

1,634.92 

51* 

161.400 

45* 

143.728 

1,643.89 

51* 

161.792 

45* 

144.121 

1,652.89 

51* 

162.185 

46 

144.514 

1,661.91 

51* 

162.578 

46* 

144.906 

1,670.95 

51* 

162.970 

462 

145.299 

1,680.02 

52 

163.363 

46| 

145.692 

1,689.11 

52* 

163.756 

46| 

146.084 

1,698.23 

52* 

164.149 

46| 

146.477 

1,707.37 

52* 

164.541 

462 

146.870 

1,716.54 

52* 

164.934 

46* 

147.262 

1,725.73 

52* 

165.327 

47 

147.655 

1,734.95 

52* 

165.719 

47* 

148.048 

1,744.19 

52* 

166.112 

47} 

148.441 

1,753.45 

53 

166.505 

47* 

148.833 

1,762.74 

53* 

166.897 

47* 

149.226 

1,772.06 

53* 

167.290 

47* 

149.619 

1,781.40 

53* 

167.6S3 

472 

150.011 

1,790.76 

53* 

168.076 

47* 

150.404 

1,800.15 

53* 

168.468 

48 

150.797 

1,809.56 

53* 

168.861 

48* 

151.189 

1,819.00 

53* 

169.251 

48* 

151.582 

1,828.46 

54 

169.646 

48* 

151.975 

1,837.95 

54* 

170.039 

48* 

152.368 

1,847.46 

54* 

170.432 

48'| 

152.760 

1,856.99 

54* 

170.824 

482 

153.153 

1,866.55 

54* 

171.217 

48* 

153.546 

1,876.14 

54* 

171.610 

49 

153.938 

1,885.75 

54* 

172.003 

49* 

154.331 

1,895.38 

54* 

172.395 

49* 

154.724 

1,905.04 

55 

172.788 

49* 

155.116 

1,914.72 

55* 

173.181 

49* 

155.509 

1,924.43 

55* 

173.573 

49* 

155.902 

1,934.16 

55* 

173.966 

492 

156.295 

1,943.91 

55* 

174.359 

49* 

156.687 

1,953.69 

55* 

174.751 

50 

157.080 

1,963.50 

55* 

175.144 

Area. 


1.973.33 

1.983.18 
1,993.06 
2,002.97 
2,012.89 
2,022.85 
2,032.82 
2,042.83 
2,052.85 
2,062.90 
2,072.98 
2,083.08 
2,093.20 
2,103.35 

2.113.52 
2,123.72 
2,133.94 

2.144.19 
2,154.46 
2,164.76 
2,175.08 
2,185.42 
2,195.79 

2.206.19 
2,216.61 
2,227.05 

2.237.52 
2,248.01 

2.258.53 
2,269.07 

2.279.64 

2.290.23 
2.300.84 

2.311.48 
2,322.15 

2.332.83 
2,343.55 
2,354.29 
2,365.05 

2.375.83 

2.386.65 

2.397.48 

2.408.34 

2.419.23 
2,430.14 
2,441.07 


TABLE  OF  CIRCLES. 


49 


Table — ( Continued). 


)iam. 

Circum. 

Area. 

55} 

175.537 

2,452.03 

56 

175.930 

2,463.01 

56} 

176.322 

2,474.02 

56} 

176.715 

2,485.05 

56} 

177.108 

2,496.11 

56} 

177.500 

2,507.19 

56} 

177.893 

2,518.30 

56^ 

178.286 

2,529.43 

56} 

178.678 

2,540.58 

57 

179.071 

2,551.76 

57} 

179.464 

2,562.97 

57} 

179.857 

2,574.20 

57  f 

180.249 

2,585.45 

57} 

180.642 

2,596.73 

57} 

181.035 

2,608.03 

57} 

181.427 

2,619.36 

57} 

181.820 

2,630.71 

58 

182.213 

2,642.09 

58} 

182.605 

2,653.49 

58} 

182.998 

2,664.91 

58} 

183.391 

2,676.36 

58} 

183.784 

2,687.84 

58} 

184.176 

2,699.33 

58} 

184.569 

2,710.86 

58} 

184.962 

2,722.41 

59 

185.354 

2,733.98 

59} 

185.747 

2,745.57 

59} 

186.140 

2,757.20 

59} 

186.532 

2,768.84 

59} 

186.925 

2,780.51 

59} 

187.318 

2,792.21 

59} 

187.711 

2,803.93 

59} 

188.103 

2,815.67 

60 

188.496 

2,827.44 

60} 

188.889 

2,839.23 

60} 

189.281 

2,851.05 

60} 

189.674 

2,862.89 

60} 

190.067 

2,874.76 

60} 

190.459 

2,886.65 

60} 

190.852 

2,898.57 

60} 

191.245 

2,910.51 

61 

191.638 

2,922.47 

61} 

192.030 

2,934.46 

61} 

192.423 

2,946.48 

61} 

192.816 

2,958.52 

61} 

193.208 

2,970.58 

iam. 

Circum. 

Area. 

61} 

193.601 

2,982.67 

61} 

193.994 

2,994.78 

61} 

194.386 

3,006.92 

62 

194.779 

3,019.08 

62} 

195.172 

3,031.26 

62} 

195.565 

3,043.47 

62} 

195.957 

3,055.71 

62} 

196.350 

3,067.97 

62} 

196.743 

3,080.25 

62} 

197.135 

3,092.56 

62} 

197.528 

3,104.89 

63 

197.921 

3,117.25 

63} 

198.313 

3,129.64 

63} 

198.706 

3,142.04 

63} 

199.099 

3,154.47 

63} 

199.492 

3,166.93 

63} 

199.884 

3,179.41 

63} 

200.277 

3,191.91 

63} 

200.670 

3,204.44 

64 

201.062 

3,217.00 

64} 

201.455 

3,229.58 

64} 

201.848 

3,242.18 

64} 

202.240 

3,254.81 

64} 

202.633 

3,267.46 

64} 

203.026 

3,280.14 

64} 

203.419 

3,292.84 

64} 

203.811 

3,305.56 

65 

204.204 

3,318.31 

65} 

204.597 

3,331.09 

65} 

204.989 

3,343.89 

65} 

205.382 

3,356.71 

65} 

205.775 

3,369.56 

65} 

206.167 

3,382.44 

65} 

206.560 

3,395.33 

65} 

206.953 

3,408.26 

66 

207.346 

3,421.20 

66} 

207.738 

3,434.17 

66} 

208.131 

3,447.17 

66} 

208.524 

3,460.19 

66} 

208.916 

3,473.24 

66} 

209.309 

3,486.30 

66} 

209.702 

3,499.40 

66} 

210.094 

3,512.52 

67 

210.487 

3,525.66 

67} 

210.880 

3,538.83 

67} 

211.273 

3,552.02 

50 


MENSURATION. 


Table  —{Continued). 


Diam. 

Circum. 

4 

Area. 

Diam. 

Circum. 

Area. 

67} 

211.665 

3.565.24 

73} 

229.729 

4,199.74 

67} 

212.058 

3,578.48 

73} 

230.122 

4,214.11 

67| 

212.451 

3,591.74 

73} 

230.515 

4,228.51 

67} 

212.843 

3,605.04 

73} 

230.908 

4,242.93 

67} 

213.236 

3,618.35 

73} 

231.300 

4,257.37 

68 

213.629 

3,631.69 

73} 

231.693 

4,271.84 

68} 

214.021 

3,645.05 

73} 

232.086 

4,286.33 

m 

„  214.414 

3,658.44 

74 

232.478 

4,300.85 

68} 

214.807 

3,671.86 

74} 

232.871 

4,315.39 

68} 

215.200 

3,685.29 

74 

233.264 

4,329.96 

68| 

215.592 

3,698.76 

74} 

233.656 

4,344.55 

68} 

215.985 

3,712.24 

74} 

234.049 

4,359.17 

68 } 

216.378 

3,725.75 

74} 

234.442 

4,373.81 

69 

216.770 

3,739.29 

74} 

234.835 

4,388.47 

69} 

217.163 

3,752.85 

74} 

235.227 

4,403.16 

69} 

217.556 

3,766.43 

75 

235.620 

4,417.87 

69} 

217.948 

3,780.04 

75} 

236.013 

4,432.61 

69} 

218.341 

3;793.68 

75} 

236.405 

4,447.38 

69} 

218.734 

3,807.34 

75} 

236.798 

4,462.16 

69} 

219.127 

3,821.02 

75} 

237.191 

4,476.98 

69} 

219.519 

3,834.73 

75} 

237.583 

4,491.81 

70 

219.912 

3,848.46 

75} 

237.976 

4,506.67 

70} 

220.305 

3,862.22 

75} 

238.369 

4,521.56 

70} 

220.697 

3,876.00 

76 

238.762 

4,536.47 

70} 

221.090 

3,889.80 

76} 

239.154 

4,551.41 

70} 

221.483 

3,903.63 

76} 

239.547 

4,566.36 

70} 

221.875 

3,917.49 

76} 

239.940 

4,581.35 

70} 

222.268 

3,931.37 

76} 

240.332 

4,596.36 

70} 

222.661 

3,945.27 

76} 

240.725 

4,611.39 

71 

223.054 

3,959.20 

76} 

241.118 

4,626.45 

71} 

223.446 

3,973.15 

76} 

241.510 

4,641.53 

71} 

223.839 

3,987.13 

77 

241.903 

4,656.64 

71} 

224.232 

4,001.13 

77} 

242.296 

4,671.77 

71} 

224.624 

4,015.16 

77| 

242.689 

4,686.92 

71} 

225.017 

4,029.21 

77} 

243.081 

4,702.10 

71} 

225.410 

4,043.29 

77} 

243.474 

4,717.31 

71} 

225.802 

4,057.39 

77} 

243.867 

4,732.54 

72 

226.195 

4,071.51 

77} 

244.259 

4,747.79 

72} 

226.588 

4,085.66 

77} 

244.652 

4,763.07 

72} 

226.981 

4,099.84 

78 

245.(115 

4,778.37 

72} 

227.373 

4,114.04 

78} 

245.437 

4,793.70 

72} 

227.766 

4,128.26 

78} 

245.830 

4,809.05 

72} 

228.159 

4,142.51 

78} 

246.223 

4,824.43 

72} 

228.551 

4,156.78 

78} 

246.616 

4,839.83 

72} 

228.944 

4,171.08 

78} 

247.008 

4,855.26 

73 

229.337 

4,185.40 

78} 

247.401 

4,870.71 

TABLE  OF  CIRCLES. 


51 


Table— ( Continued) 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

78} 

247.794 

4,886.18 

84} 

265.858 

5,624.56 

79 

248.186 

4,901.68 

84} 

266.251 

5,641.18 

79} 

248.579 

4,917.21 

84} 

266.643 

5,657.84 

79} 

248.972 

4,932.75 

85 

267.036 

5,674.51 

79* 

249.364 

4,948.33 

85} 

267.429 

5,691.22 

79} 

249.757 

4,963.92 

85} 

267.821 

5,707.94 

79* 

250.150 

4,979.55 

85} 

268.214 

5,724.69 

79} 

250.543 

4,995.19 

85} 

268.607 

5,741.47 

79} 

250.935 

5,010.86 

85} 

268.999 

5,758.27 

80  * 

251.328 

5,026.56 

85} 

269.392 

5,775.10 

80} 

251.721 

5,042.28 

85} 

269.785 

5,791.94 

80} 

252.113 

5,058.03 

86 

270.178 

5,808.82 

80} 

252.506 

5,073.79 

86} 

270.570 

5,825.72 

80} 

252.899 

5,089.59 

86} 

270.963 

5,842.64 

80} 

253.291 

5,105.41 

86} 

271.356 

5,859.59 

80} 

253.684 

5,121.25 

86} 

271.748 

5,876.56 

80} 

254.077 

5,137.12 

86} 

272.141 

5,893.55 

81 

254.470 

5,153.01 

86} 

272.534 

5,910.58 

81} 

254.862 

5,168.93 

86} 

272.926 

5,927.62 

81} 

255.255 

5,184.87 

87 

273.319 

5,944.69 

81}  * 

255.648 

5,200.83 

87} 

273.712 

5,961.79 

81} 

256.040 

5,216.82 

87} 

274.105 

5,978.91 

81} 

256.433 

5,232.84 

87} 

274.497 

5,996.05 

81} 

256.826 

5,248.88 

87} 

274.890 

6,013.22 

81} 

257.218 

5,264.94 

87} 

275.283 

6,030.41 

82 

257.611 

5,281.03 

87} 

275.675 

6,047.63 

82} 

258.004 

5,297.14 

87} 

276.068 

6,064.87 

82} 

258.397 

5,313.28 

88 

276.461 

6,082.14 

82} 

258.789 

5,329.44 

88} 

276.853 

6,099.43 

82} 

259.182 

5,345.63 

88} 

277.246 

6,116.74 

82} 

259.575 

5,361.84 

88} 

277.629 

6,134.08 

82} 

259.967 

5,378.08 

88} 

278.032 

6,151.45 

82} 

260.360 

5,394.34 

88} 

278.424 

6.168.84 

83 

250.753 

5,410.62 

88} 

278.817 

6,186.25 

83} 

261.145 

5,426.93 

88} 

279.210 

6,203.69 

83} 

261.538 

5,443.26 

89 

279.602 

6,221.15 

83} 

261.931 

5,459.62 

89} 

279.995 

6,238.64 

83} 

262.324 

5,476.01 

89} 

280.388 

6,256.15 

83} 

262.716 

5,492.41 

89} 

280.780 

6,273.69 

83} 

263.109 

5,508.84 

89} 

281.173 

6,291.25 

83} 

263.502 

5,525.30 

89} 

281.566 

6,308.84 

84 

263.894 

5,541.78 

89} 

281.959 

6,326.45 

84} 

264.287 

5,558.29 

89} 

282.351 

6,344.08 

84 

264.680 

5,574.82 

90 

282.744 

6,361.74 

84} 

265.072 

5,591.37 

90} 

283.137 

6,379.42 

84} 

265.465 

5,607.95 

90} 

283.529 

6,397.13 

52 


MENSURATION. 


Table —  ( Continued ) . 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

90| 

283.922 

6,414.86 

95} 

299.237 

7,125.59 

90} 

284.315 

6,432.62 

95} 

299.630 

7,144.31 

90| 

284.707 

6,450.40 

95} 

300.023 

7,163.04 

90| 

285.100 

6,468.21 

95} 

300.415 

7,181.81 

90| 

285.493 

6,486.04 

95} 

300.808 

7,200.60 

91 

285.886 

6,503.90 

95} 

301.201 

7,219.41 

91} 

286.278 

6,521.78 

96 

301.594 

7,238.25 

91} 

286.671 

6,539.68 

96} 

301.986 

7,257.11 

91} 

287.064 

6,557.61 

96} 

302.379 

7,275.99 

91} 

287.456 

6,575.56 

96} 

302.772 

7,294.91 

91| 

287.849 

6,593.54 

96} 

303.164 

7,313.84 

91} 

288.242 

6,611.55 

96} 

303.557 

7,332.80 

91} 

288.634 

6,629.57 

96} 

303.950 

7,351.79 

92 

289.027 

6,647.63 

96} 

304.342 

7,370.79 

92} 

289.420 

6,665.70 

97 

304.735 

7,389.83 

92} 

289.813 

6,683.80 

97} 

305.128 

7,408.89 

92} 

290.205 

6,701.93 

97} 

305.521 

7,427.97 

92} 

290.598 

6,720.08 

97} 

305.913 

7,447.08 

92} 

290.991 

6,738.25 

97} 

306.306 

7,466.21 

92} 

291.383 

6,756.45 

97} 

306.699 

7,485.37 

92} 

291.776 

6,774.68 

97} 

307.091 

7,504.55 

93 

292.169 

6,792.92 

97} 

307.484 

7,523.75 

93} 

292.562 

6,811.20 

98 

307.877 

7.542.98 

93} 

292.954 

6,829.49 

98} 

308.270 

7,562.24 

93} 

293.347 

6,847.82 

98} 

308.662 

7,581.52 

93} 

293.740 

6,866.16 

98} 

309.055 

7,600.82 

93} 

294.132 

6,884.53 

98} 

309.448 

7,620.15 

93} 

294.525 

6,902.93 

98} 

309.840 

7,639.50 

93} 

294.918 

6,921.35 

98} 

310.233 

7,658.88 

94 

295.310 

6,939.79 

98} 

310.626 

7,678.28 

94} 

295.703 

6,958.26 

99 

311.018 

7,697.71 

94} 

296.096 

6,976.76 

99} 

311.411 

7,717.16 

94} 

296.488 

6,995.28 

99} 

311.804 

7,736.63 

94} 

296.881 

7,013.82 

99} 

312.196 

7,756.13 

94} 

297.274 

7,032.39 

99} 

312.589 

7,775.66 

94} 

297.667 

7,050.98 

99} 

312.982 

7,795.21 

94} 

298.059 

7,069.59 

99} 

313.375 

7,814.78 

95 

298.452 

7,088.24 

99} 

313.767 

7,834.38 

95} 

298.845 

7,106.90 

100 

314.160 

7,854.00 

The  preceding  table  may  be  used  to  determine  the 
diameter  when  the  circumference  or  area  is  known.  Thus, 
the  diameter  of  a  circle  having  an  area  of  7,200  sq.  in.  is, 
approximately,  95}  in. 


TABLES  OF  DECIMALS. 


53 


DECIMAL  EQUIVALENTS  OF  PARTS  OF  ONE  INCH. 


1-64 

.015625 

17-64 

.265625 

33-64 

.515625 

49-64 

.765625 

1-32 

.031250 

9-32 

.281250 

17-32 

.531250 

25-32 

.781250 

3-64 

.046875 

19-64 

.296875 

35-64 

.546875 

51-64 

.796875 

1-16 

.062500 

5-16 

.312500 

9-16 

.562500 

13-16 

.812500 

5-64 

.078125 

21-64 

.328125 

37-64 

.578125 

53-64 

.828125 

3-32 

.093750 

11-32 

.343750 

19-32 

.593750 

27-32 

.843750 

7-64 

.109375 

23-64 

.359375 

39-64 

.609375 

55-64 

.859375 

1-8 

.125000 

3-8 

.375000 

5-8 

.625000 

7-8 

.875000 

9-64 

.140625 

25-64 

.390625 

41-64 

.640625 

57-64 

.890625 

5-32 

.156250 

13-32 

.406250 

21-32 

.656250 

29-32 

.906250 

11-64 

.171875 

27-64 

.421875 

43-64 

.671875 

59-64 

.921875 

3-16 

.187500 

7-16 

.437500 

11-16 

.687500 

15-16 

.937500 

13-64 

.203125 

29-64 

.453125 

45-64 

.703125 

61-64 

.953125 

7-32 

.218750 

15-32 

.468750 

23-32 

.718750 

31-32 

.968750 

15-64 

.234375 

31-64 

.484375 

47-64 

.734375 

63-64 

.984375 

1-4 

.250000 

1-2 

.500000 

3-4 

.750000 

1 

1 

DECIMALS  OF  A  FOOT  FOR  EACH  1-32  OF  AN  INCH. 


Inch. 

0" 

1" 

2" 

3" 

4" 

5" 

0 

0 

.0833 

.1667 

.2500 

.3333 

.4167 

.0026 

.0859 

.1693 

.2526 

.3359 

.4193 

"Tfc 

.0052 

.0885 

.1719 

.2552 

.3385 

.4219 

5^ 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

.0104 

.0937 

.1771 

.2604 

.3437 

.4271 

.0130 

.0964 

.1797 

.2630 

-.3464 

.4297 

.0156 

.0990 

.1823 

.2656 

.3490 

.4323 

.0182 

.1016 

.1849 

.2682 

.3516 

.4349  * 

.0208 

.1042 

.1875 

.2708 

.3542 

.4375 

32 

.0234 

.1068 

.1901 

.2734 

.3568 

.4401 

TS 

.0260 

.1094 

.1927 

.2760 

.3594 

.4427 

if 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

JL 

.0312 

.1146 

.1979 

.2812 

.3646 

.4479 

if 

.0339 

.1172 

.2005 

.2839 

.3672 

.4505 

TS 

.0365 

.1198 

.2031 

.2865 

.3698 

.4531 

if 

.0391 

.1224 

.2057 

.2891 

.3724 

.4557 

l 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

if 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

if 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

if 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

\h 

.0573 

.1406 

.2240 

.3073 

.3906 

.4740 

U 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

54 


MENSURATION. 


Table — ( Continued). 


Inch. 

0" 

1" 

2" 

3" 

4" 

5" 

1 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

ft 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

if 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

U 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

7 

T 

.0729 

.1562 

.2396 

.3229 

.4062 

.4896 

M 

.0755 

.1589 

.2422 

.3255 

.4089 

.4922 

it 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

u 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

DECIMALS  OF  A  FOOT  FOR  EACH  1-32  OF  AN  INCH, 


Inch. 

6" 

7" 

8" 

9" 

10" 

11" 

0 

.5000 

.5833 

.6667 

.7500 

.8333 

.9167 

3*5 

.5026 

.5859 

.6693 

.7526 

.8359 

.9193 

1*5 

.5052 

.5885 

.6719 

.7552 

.8385 

.9219 

3% 

.5078 

.5911 

.6745 

.7578 

.8411 

.9245 

.5104 

.5937 

.6771 

.7604 

.8437 

.9271 

3% 

.5130 

.5964 

.6797 

.7630 

.8464 

.9297 

T5 

.5156 

.5990 

.6823 

.7656 

.8490 

.9323 

35 

.5182 

.6016 

.6849 

.7682 

.8516 

.9349 

i_ 

.5208 

.6042 

.6875 

.7708 

.8542 

.9375 

& 

.5234 

.6068 

.6901 

.7734 

.8568 

.9401 

TU 

.5260 

.6094 

.6927 

.7760 

.8594 

.9427 

32 

.5286 

.6120 

.6953 

.7786 

.8620 

.9453 

§ 

.5312 

.6146 

.6979 

.7812 

.8646 

.9479 

if 

.5339 

.6172 

.7005 

.7839 

.8672 

.9505 

T?3 

.5365 

.6198 

.7031 

.7865 

.8698 

.9531 

if 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

2 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

tf 

.5443 

.6276 

.7109 

.7943 

.8776 

.9609 

T95 

.5469 

.6302 

.7135 

.7969 

.8802 

.9635 

if 

.5495 

.6328 

.7161 

.7995 

.8828 

.9661 

i 

.5521 

.6354 

.7188 

.8021 

.8854 

.9688 

3* 

.5547 

.6380 

.7214 

.8047 

.8880 

.9714 

if 

.5573 

.6406 

.7240 

.8073 

.8906 

.9740 

33 

.5599 

.6432 

.7266 

.8099 

.8932 

.9766 

* 

.5625 

.6458 

.7292 

.8125 

.8958 

.9792 

if 

.5651 

.6484 

.7318 

.8151 

.8984 

.9818 

if 

.5677 

.6510 

.7344 

.8177 

.9010 

.9844 

§5 

.5703 

.6536 

.7370 

.8203 

.9036 

.9870 

7 

e 

.5729 

.6562 

.7396 

.8229 

.9062 

.9896 

if 

.5755 

.6)589 

.7422 

.8255 

.9089 

.9922 

if 

.5781 

.6615 

.7448 

.8281 

.9115 

.9948 

33 

.5807 

.6641 

.7474 

.8307 

.9141 

.9974 

GEOMETRICAL  DRAWING. 


55 


GEOMETRICAL  DRAWING. 


> 


4- 


To  erect  a  perpendicular  to  the  line  b  c 
at  the  point  a.  With  a  as  a  center,  and 
any  radius,  as  ab,  strike  arcs  cutting  the 
line  at  b  and  c.  From  b  and  c  as  centers, 
and  any  radius  greater  than  b  a,  strike 
arcs  intersecting  at  d.  Draw  d  a,  which 
will  be  perpendicular  to  b  c  at  a. 

To  draw  a  line  parallel  to  a  b.  At  any 
points  a  and  5,  with  a  radius  equal  to  the 
required  distance  between  thelines.draw 

_ _ -  arcs  at  c  and  d.  The  line  c  d ,  tangent  to 

.  the  arcs,  will  be  the  required  parallel. 

To  bisect  the  angle  b  a  c.  With  a  as  a 
center,  strike  an  arc  cutting  the  sides  of 
i  the  angle  in  b  and  c.  With  b  and  c  as 
centers,  and  any  radius,  strike  arcs  inter¬ 
secting,  as  at  d.  Draw  d  a,  the  bisector. 

To  erect  a  perpendicular  at  the  end  of  a  line. 
d\  Take  a  center  anywhere  above  the  line,  as  at 
^  b.  Strike  an  arc  passing  through  a  and 
j  cutting  the  given  line  at  c.  Draw  a  line 
ji  through  c  and  b,  cutting  the  arc  at  d.  Draw 
the  line  ad,  which  will  be  the  required 
perpendicular. 

To  divide  a  line  into  any  number  of  equal  parts.  Let  it  be 
required  to  divide  the  line  ab  into  5  equal  j>arts.  Draw  any 
line  a  d,  and  point  off  5  equal  divisions, 
as  shown.  From  5  draw  a  line  to  b  and 
draw  4-4',  5-3',  etc.  parallel  to  5  b. 

To  divide  a  space  between  two  parallel 
lines  or  surfaces  (for  example,  the  spa¬ 
cing  of  risers  in  a  stairway).  Draw  a  b 
andce  the  given  distance  apart.  Then  move  a  scale  along 
them,  until  as  many  spaces  are  included  along  a  d  as  there  are 
number  of  divisions  required.  Mark  the  points  1 ,  5, 3,  etc., 
and  draw  lines  through  them  parallel  to  ab  and  ce. 


/ 


56 


GEOMETRICAL  DR  A  WING. 


The  magnitude  of  an  angle  depends 
not  upon  the  length  of  its  sides,  hut 
upon  the  number  of  degrees  contained 
in  the  arc  of  a  circle  drawn  with  the 
vertex  as  a  center.  The  circle  is  divided 
into  360  equal  parts,  called  degrees.  To 
divide  a  quadrant  as  shown  in  the  fig’ 
ure,  first  divide  it  into  3  parts  by  the 
arcs  at  e  and  d,  chords  e  d  and  a  e  being 
equal  to  the  radius.  Then  subdivide  with  dividers. 

An  inscribed  angle  has  its  vertex  (as 
c  or  d)  in  the  circumference  of  a  circle. 

Any  angle  inscribed  in  a  semicircle  is 
a  right  angle,  as  a  c  b,  or  a  d  b. 

To  draw  a  circle  through  three  points  not  in  a  straight  line ,  as 
a,  b,  and  c.  Bisect  a  b  and  also  b  c. 
The  two  bisectors  will  intersect  in  a 
point  d,  which  will  be  the  center  of  the 
required  circle. 

To  find  the  center  of  a  circular  arc,  as 
abc,  take  a  point,  as  b  on  the  curve, 
and  draw  ba  and  be.  Bisect  these 
lines  by  perpendiculars ;  the  intersec¬ 
tion  d  will  be  the  required  center. 

To  find  a  straight  line  nearly  equal  to 
a  semi-circumference,  as  abc.  On  the 
diameter  construct  the  equilateral  tri¬ 
angle  a  c  li.  Through  a  and  c  draw  h  e 
and  hf.  Then  e f  is  the  length  of  the 
semi-circumference.  Draw  any  line,  as 
hkl;  then  If  is  almost  exactly  the 
length  of  arc  k  c,  and  b  l  that  of  arc  b  k. 

To  construct  a  hexagon  from  a  given  side . 
Describe  a  circle  with  a  radius  a  b  equal  to 
the  given  side.  Draw  a  diameter  as  cb. 
From  c  and  b  as  centers,  and  a  radius  equal 
to  the  given  side,  draw  arcs  cutting  the 
circle  at  k,d,f  and  e.  Connect  c,  k,f,  b, 
e,  and  d. 


GEOMETRICAL  ERA  WING. 


57 


To  inscribe  an  octagon  i n  a  square.  Draw 
the  diagonals  ac  and  bd.  With  a  as  a 
center,  and  ae  as  a  radius,  strike  an  arc 
cutting  the  sides  of  the  square  at  /  and  h. 

Repeat  the  operation  at  b,  c,  and  d,  and 
draw  lines  connecting  the  eight  points 
thus  found  to  form  the  figure  required. 

To  draw  any  regular  polygon  in  a  circle. 
Divide  360°  by  the  number  of  sides ;  the 
quotient  will  be  the  angle  aob.  Lay  off 
this  angle  at  the  center  with  a  protractor, 
and  draw  its  chord,  a  side  of  the  required 
polygon.  Step  this  side  around  on  the  cir¬ 
cumference,  and  connect  the  points  found. 

To  draw  a  segment  of  a  circle ,  having  given  the  chord  a  b  and 
height  c d.  Draw  ef,  through  d,  parallel  to  ah  ;  also,  a d  and 
db.  Draw  a e  and  bf  perpendicular  to  e  k  d  k  f 

a  d  and  d  b  ;  also  a  h  and  b  k  perpendic-  \  / 

ular  to  ab.  Divide  ed,  df,  ac,  cb,  ah,  'ffx  \  \  i  /  /  yki/' 

and  6  &  into  the  same  number  of  equal  °  c  6 

parts.  Draw  lines  connecting  the  points  as  shown,  and  trace 
the  curve  through  the  intersections. 

To  draw  a  segment  of  a  circle  by  means  of  a  fixed  triangle. 
Let  a  5  be  the  required  chord,  and  d  c  the  rise.  Drive  nails  at 

a  and  b.  Make  a  triangle,  as  shown, 
from  thin  strips,  so  that  the  vertex 
comes  at  c,  and  stiffen  it  with  the  cross- 
biace.  Now,  by  moving  the  triangle, 
always  keeping  the  sides  touching  the  nails  at  a  and  b,  the 
arc  may  be  traced  by  a  pencil  held  at  c. 

To  draw  an  ellipse,  having  given  the 
axes.  Draw  concentric  circles  whose 
diameters  are  equal  to  the  axes  ab 
and  cd.  From  o  draw  any  radius,  as 
oe.  From  g,  where  oe  cuts  the  inner 
circle,  draw  gf  parallel  to  the  major 
axis  ab.  From  e,  draw  ef  parallel  to 
the  minor  axis  d  c.  The  intersection  / 
gives  a  point  on  the  ellipse.  Other  points  are  similarly  found. 


58 


GEOMETRICAL  DR  A  WING. 


To  draw  an  ellipse  with  a  string,  having  given  the  axes  ab 
and  c  d.  With  c  as  a  center,  and  a  radius 
equal  to  o  b,  strike  arcs  cutting  the  major 
axis  at  e  and  /,  the  foci  of  the  ellipse. 
Stick  pins  at  e  and  /,  and  attach  a  string 
as  shown,  the  length  of  the  string  being 
equal  to  the  length  of  the  major  axis. 
Keep  the  string  stretched  with  a  pencil 
point,  and  sweep  around  the  ellipse. 

To  draw  a  parabola.  Having  given  the 
coordinates  a  b  and  b  c,  to  draw  a  parabola, 
complete  the  rectangle  abed.  Divide  b c 
and  cd  into  the  same  number  of  equal 
parts.  From  1' ,  2',  S',  etc.,  draw  lines 
through  a.  Through  1,  2,  3,  etc.,  draw 
lines  parallel  to  a  b.  The  intersections  of 
1'  a  and  1-1",  of  2'  a  and  2-2",  etc.  are 
points  on  the  required  parabola. 

To  draiv  a  hyperbola.  Hating  given  the 
coordinates  a  b  and  b  c,  to  draw  the  curve. 
Complete  the  rectangle  abed,  and  divide  b c 
and  c  d  into  the  same  number  of  equal  parts. 
Select  any  point  e  on  the  line  b  a  prolonged  ; 
as  e  is  taken  farther  from  a,  the  hyperbola 
will  approach  a  parabola  in  form.  Connect 
1,  2,  S  to  e,  and  1',  2',  S'  to  a.  The  intersec¬ 
tions  of  le  and  l'a,  of  2e  and  2' a,  etc.  are 
points  on  the  required  hyperbola. 

To  draw  a  spiral.  From  a  point,  as 
o,  draw  radiating  lines,  oa,ob,o  c,  etc., 
making  equal  angles  with  each  other. 

At  any  point,  as  d,  on  oa,  start  the 
spiral  by  drawing  de  perpendicular  to 
o  a  ;  from  e  where  d  e  intersects  o  b, 
draw  ef  perpendicular  to  ob ;  etc.  By 
making  the  angle  between  the  lines 
smaller,  the  spiral  may  be  made  to 
make  more  turns,  and  the  broken  line 
will  approach  more  nearly  to  a  curve. 


GEOMETRICAL  DRAWING. 


59 


To  draw  a  spiral ,  second  method.  Draw  a  small  circle,  as 
bfa.  Divide  the  circumference  into  any 
number  of  equal  parts,  eight  or  more. 

Draw  tangents  at  the  points  of  division, 
as  be,  de,  etc.  With  b  as  a  center,  and 
ba  as  a  radius,  strike  the  arc  ac.  With 
d  as  a  center,  and  d  c  as  a  radius,  strike 
the  arc  ce,  etc.  This  method  is  a  very 
close  approximation,  though  not  mathe¬ 
matically  correct. 

The  Roman  Ionic  volute.  For  the  eye,  draw  the  small  circle, 
taking  \  the  distance  between  ab  and  cd,  in  ( b ),  as  its 

diameter.  In  (a)  is 
shown  the  eye  en¬ 
larged.  Mark  points  1 
and  2,  at  the  middle  of 
/ c  and / d.  Divide  2-12 
"into  three  parts  b  y 
points  6  and  10.  At  a 
distance  below  cd  equal 
to  2k  times  the  space 
between  2-1  and  6-5, 
draw  3- 4.  Draw  1-12, 
10-9,  2-3,  and  5-4.  Draw  45°  lines  from  3  and  4;  draw  6-7, 
10-11,  9-8,  11-12,  and  7-8.  Use  the  points  thus  found  as 
centers,  1  being  the  center  for  arc  ae;  2  for  arc  eg;  3  for 
arc  gf\  etc. 

To  draw  a  helix.  A  helix  is  the  curve  assumed  by  a  straight 

line,  as  d  f,  drawn  on  a 
plane,  when  the  plane  is 
wrapped  around  a  cylin¬ 
drical  surface.  To  draw 
a  helix,  having  given  the 
plan  of  the  cylinder  a  be 
and  the  rise  c'  c",  divide  the  arc  a  be  into  any 
number  of  equal  parts,  as  at  1,  2,  b,  etc.  Di\  ide 
c'  c"  into  the  same  number  of  equal  parts. 
Draw  verticals  through  the  divisions  of  the  arc 
abc,  and  horizontals  through  the  divisions  of 


~rr 

i/ 

iw 

60 


GEOMETRICAL  ERA  WING. 


c ’  c",  intersecting  in  points  1 ',  2' ,  b",  etc.  Other  points  may 
be  similarly  found  and  the  curv.e  drawn. 

To  develop  the  surface  of  a  cylinder  cut  by  a  plane  oblique  to 
,,  the  axis.  Let  abc  be  the 

f  plan  of  the  cylinder,  and 
a'  c"  the  inclination  of 
the  cutting  plane. 
Divide  the  arc  abc  into 
a  n  y  number  of  equal 
etc.  Draw  d  e  equal  to  the 
3,  and  mark  the  same  divi- 
e,  as  dl ",  l"-2",  etc.  Draw 
;lirough  points  1',  2',  etc., 
intersecting  verticals  drawn  through  1 ",  2", 
etc.,  as  shown.  Trace  a  curve  through  the  points  d,  1"',  2"', 
etc.,  and  the  figure  dfe  will  be  the  development  of  the  half 
cylinder  abc. 


LAYING  OUT  ANGLES. 

By  Two-Foot  Rule. — To  lay  off  any  angle  given  in  the  table, 
open  the  rule  at  the  middle  until  the  distance  between  the 
inside  corners  at  the  knuckle  joints  (6-inches’  mark)  is  equal 
to  the  distance  given  for  that  angle  under  Chord. 


Degrees. 

Chord. 

Inches. 

Degrees. 

Chord. 

Inches. 

5 

hi 

50 

10 

1  35 

55 

bhl 

15 

la95 

60 

6 

20 

O  3 
^33 

65 

6/, 

65 

25 

9  9 
~33 

70 

30 

35 

3  35 

351 

75 

80 

7t68 

7§f 

40 

4& 

85 

85 

45 

451 

90 

85 

To  lay  off  an  angle  greater  than  90°,  subtract  the  angle 
from  180° ;  lay  out  the  latter  angle,  extending  one  side,  so 
that  the  greater  angle  formed  will  be  the  one  required. 


GEOMETRICAL  ERA  WING. 


61 


By  Steel  Square.— To  lay  off*  any  angle  given  in  the  table,  set 
either  blade  or  tongue  of  the  square  along  the  line  a  b,  mark¬ 
ing  the  12"  point  at  a.  Mark  c  at  a  distance  from  b  equal  to 


that  given  in  the  table  for  the  required  angle,  and  draw  a  c ; 
then  the  angle  bac  will  be  the  angle  sought,  approximately 
correct. 


For  example,  to  find  an  angle  of  30°,  the  distance  b  c  is 
611  in. 


Angle. 

Degrees. 

Distance. 

Inches. 

Angle. 

Degrees. 

Distance. 

Inches. 

5 

1ft 

33°  42' 

Q 

10 

2ft 

(1  pitch) 

15 

q  7 
^32 

35 

m 

18°  25' 

A 

40 

loft 

(1  pitch  roof) 

45 

12 

20 

41 

(1  pitch) 

221 

50 

14ft 

25 

£19 

°32 

53°  7' 

16 

26°  33' 

a 

(f  pitch) 

(1  pitch) 

D 

55 

171 

30 

t M  5 

60 

20  if 

Taking  a  at  the  3"  Mark. 


65 

6ft 

75 

lift 

671 

71 

80 

17 

(Octagon  Cut) 

Angle 

70 

81 

90 

abc 

£ 


62 


STRUCTURAL  DESIGN. 


STRUCTURAL  DESIGN. 

LOADS  ON  STRUCTURES. 

Loads  on  buildings  may  be  classed  under  three  general 
divisions :  dead  loads,  live  loads,  and  snow  and  wind  loads. 


DEAD  LOADS. 

The  dead  loads  consist  of  the  weight  of  the  materials  com¬ 
posing  the  structure.  For  instance,  the  brickwork  in  the 
walls  forms  a  portion  of  the  dead  load  upon  the  footings; 
the  materials  in  the  floors  impose  a  dead  load  upon  the 
columns,  etc.  In  order  to  figure  the  amount  of  the  dead 
loads  on  structures  and  the  members  therein,  the  weight  of 
the  various  materials  used  must  be  known,  and  the  following 
tables  will  be  found  useful.  (For  weights  of  metals,  masonry, 
woods,  etc.,  see  pages  29,  30,  and  31.) 

TABLE  I. 

Approximate  Weight  of  Building  Materials. 


Material. 


Average 
Weight.  Lb. 
per  Sq.  Ft. 


Corrugated  galvanized  iron,  No.  20,  unboarded 

Copper,  16  oz.,  standing  seam  . 

Felt  and  asphalt,  without  sheathing . 

Glass,  £  in.  thick . 

Hemlock  sheathing,  1  in.  thick  . 

Lead,  about  }  in.  thick...., . 

Lath-and-plaster  ceiling  (ordinary) . 

Mackite,  1  in.  thick,  with  plaster  * . 

Neponset  roofing  felt,  2  layers . 

Spruce  sheathing,  1  in.  thick  . 

Slate,  t3g  in.  thick,  3  in.  double  lap . a . 

Slate,  £  in.  thick,  3  in.  double  lap . * . 

Shingles,  6"  X  18",  4  to  weather . 

Skylight  of  glass,  T35  to  £  in.,  including  frame... 

Slag  roof,  4-ply . . . 

Tin,  IX  . 

Tiles  (plain),  104"  X  6i"  X  I"  —  51"  to  weather 
Tiles  (Spanish),  144"  x  104"  —  74"  to  weather... 

White-pine  sheathing,  1  in.  thick  . 

Yellow-pine  sheathing,  1  in.  thick  . 


“4 

H 

2 

If 

2 

6  to  8 
6  to  8 
10 
* 

2* 

6f 

44 

2 

4  to  10 
4 
f 

18 

84 

24 

4 


LOADS  ON  STRUCTURES. 


63 


Where  only  the  approximate  dead  load  due  to  the  weight 
of  floor,  partition,  or  roof  construction  is  desired,  the  follow- 
ing  table  will  be  of  use.  In  this  table  the  wooden  floors  and 
roof  sheathing  are  taken  as  1  in.  thick. 


TABLE  II. 

Weight  of  Floors,  Partitions,  and  Roofs. 


Material. 

Weight. 
Lb.  per 

Sq.  Ft. 

Floors,  including  weight  of  beams — 

Wooden,  in  dwellings . 

Wooden,  office  buildings  . . 

Hollow-tile  arch . 

Brick  and  concrete  (broken  stone)  . 

Partitions — 

Wooden  . 

Hollow  tile . . 

Roofs,  including  f  raming — 

Shingle  . . . 

Tin  . 

10-15 

25-30 

70-90 

100-130 

15-20 

15-30 

6-10 

6-  8 

Sla.te  .  -  . 

12-15 

Tnr  fmrl  crrnvpl  . 

10-12 

P!nrrii  P’fl.t.pd  iron  . 

8-10 

Tile  . 

20-30 

Note. — If  roofs  are  plastered  underneath,  add  6  pounds 
per  square  foot  to  the  weight  given. 


In  calculating  the  dead  loads,  there  are  certain  weights 
which  must  be  assumed.  For  instance,  the  weight  of  the 
floorbeams  and  girders  are  not  known,  because  their  size 
has  not  as  yet  been  determined ;  likewise,  the  dimensions  of 
the  columns  and  many  other  structural  details  are  unknown. 
The  assumed  weights  are  obtained  by  approximating  the 
dimensions  of  the  parts  of  the  structure  and  estimating  their 
weights.  After  the  structure  has  been  designed,  the  actual 
dead  loads  should  be  checked,  to  make  sure  they  approxi¬ 
mate  closely  to  those  assumed.  If  any  considerable  variation 
is  found,  it  can  be  taken  care  of  by  increasing  or  diminishing 
the  sizes  already  determined. 


64 


STRUCTURAL  DESIGN. 


Weight  of  Fireproof  Floors.— In  figuring  the  dead  load  for 
any  system  of  floor  construction,  it  is  necessary  to  carefully 
calculate  the  total  weight  of  the  elements  composing  the 
system,  which  are  the  arches,  filling,  flooring,  ceiling,  and  the 
steel  construction.  The  weight  of  fixed  or  permanent  parti¬ 
tions  should  always  be  taken  into  account,  and  the  beams,  etc. 
carrying  them,  proportioned  accordingly.  Where  the  parti¬ 
tions  are  movable,  an  additional  weight  of,  say,  20  lb.  per  sq. 
ft.,  should  be  added  to  the  dead  load  on  the  entire  floor  area. 
The  finished  floor  line  is  usually  considered  as  being  3  in.  above 
the  top  of  the  I  beams,  and  the  ceiling  line  as  2  in.  below  the 
bottom  of  them.  Cinder  concrete  filling,  which  is  the  usual 
backing  for  fireproof  arch  construction,  averages  in  weight, 
when  dry,  72  lb.  per  cu.  ft.,  but  is  sometimes  assumed  to  weigh 
only  48  lb.  per  cu.  ft. 

The  weight  of  the  various  systems  of  fireproof  floors  vary 
from  60  lb.  to  125  lb.  per  sq.  ft.  of  floor  surface,  including  the 
steel  used ;  generally,  however,  a  load  of  80  lb.  per  sq.  ft.  will 
be  sufficient  for  all  economical  fireproof  floors. 


TABLE  III. 

Approximate  Weight  of  Fireproof  Floors. 
( Exclusive  of  Partitions.) 


Depth  of 

I  Beams. 

Weight.  Lb.  per  Sq. Ft.  Including  Beams. 

Brick  Arch. 

Hollow  Tile. 

8 

74 

63-  74 

9 

74 

65—  80 

10 

81 

68-  81 

12 

94 

71-  93 

15 

113 

91-113 

Semi-fireproof  floors,  supported  upon  I  beams  placed  5  ft. 
apart  crossed  every  4  ft.  with  heavy  T’s,  constructed  of 
buckled  plates  i  in.  thick  and  covered  with  6  in.  of  concrete 
composed  of  broken  stone  and  cement,  imbedding  sleepers  to 
which  l  in.  finished  floor  is  secured,  weigh,  approximately 
95  lb.  per  sq.  ft. 


LOADS  ON  STRUCTURES. 


6d 


TABLE  IV. 

Weight  of  Fireproofing  Materials. 


Kind. 

Span. 

Ft. 

Thickness. 

In. 

Weight.  Lb. 
per  Sq.  Ft. 

Dense-tile  flat  arch  . 

4-  7 

6-12 

22-42 

Porous-tile  flat  arch . 

3-10 

6-15 

21-43 

Dense-tile  partition . 

3-  6 

15-28 

Porous-tile  partition . 

3-  6 

14-27 

Porous-tile  ceiling . 

2-  4 

12-20 

Porous-tile  roofing . 

2-  4 

12-20 

LIVE  LOADS. 

The  live  load  is  variable,  and  consists  of  the  weight  of 
people,  furniture,  stocks  of  goods,  machinery,  etc.  The 
amount  of  this  load,  which  should  be  added  to  the  dead  load, 
depends  upon  the  use  to  which  the  building  is  to  be  put. 
Where  the  floor  is  required  to  support  a  considerable  live 
load,  concentrated  at  a  particular  place,  such  as  a  heavy  safe 
or  piece  of  machinery,  special  provision  should  he  made  in 
the  floor  construction  for  it.  Table  V  gives  the  live  loads  per 
square  foot  recommended  as  good  practice  in  conservative 
building  construction. 


TABLE  V. 


Live  Loads. 

Lb.  per  Sq.  Ft. 

Dwellings,  offices,  hotels,  and  apart¬ 
ment  houses  . 

Theaters,  churches,  ballrooms,  and 

drill  halls . 

Factories  . 

Warehouses . 

From  40  to  70 

From  80  to  120 

From  150  up 

From  150  to  250 

A  live  load  of  70  lb.  per  sq.  ft.  will  seldom  be  attained 
in  dwellings;  hut,  as  city  houses  are  liable  to  be  used  for 
other  than  dwelling  purposes,  it  is  not  generally  advisable  to 


66 


STRUCTURAL  DESIGN. 


use  a  lighter  load.  In  country  houses,  hotels,  etc.,  where 
economy  demands  it,  and  the  intended  use  for  a  long  time  is 
certain,  a  live  load  of  40  lb.  per  sq.  ft.  of  floor  surface  is  ample 
for  all  rooms  not  used  for  public  assembly.  For  such  rooms, 
a  live  load  of  80  lb.  per  sq.  ft.  will  usually  be  sufficient,  as 
experience  shows  that  a  floor  cannot  be  crowded  more  than 
this.  If  the  desks  and  chairs  are  fixed,  as  in  a  schoolroom  or 
church,  a  live  load  over  40  to  50  lb.  will  never  be  attained. 

Office-building  floors  have  been  designed  for  a  live  load 
ranging  from  20  to  150  lb.  per  sq.  ft.,  but  a  conservative  prac¬ 
tice  is  to  use  about  70  lb.  per  sq.  ft.  An  investigation  of  the 
live  loads  in  over  200  office  buildings  in  Boston  showed 
that  the  greatest  live  load  in  any  office  was  40  lb.  per  sq.  ft., 
while  the  10  heaviest  loaded  offices  averaged  33  lb.  per 
sq.  ft.,  the  average  live  load  for  the  entire  number  of  offices 
being  about  17  lb.  per  sq.  ft. 

Retail  stores  should  have  floors  proportioned  for  a  live 
load  of  100  lb.  and  upwards;  while,  for  wholesale  stores, 
machine  shops,  etc.,  a  live  load  of  at  least  150  lb.  per  sq.  ft. 
should  be  figured  on.  The  static  load  in  factories  seldom 
exceeds  40  to  50  lb.  per  sq.  ft.  of  floor  surface,  and  usually  a 
live  load  of  100  lb.,  including  the  effect  of  vibrations  due  to 
moving  machinery,  is  ample.  The  conservative  rule  is,  in 
general,  to  assume  loads  not  less  than  the  above,  and  to  be 
sure  that  the  beams  are  proportioned  to  avoid  excessive 
deflection.  Stiffness  is  a  factor  as  important  as  mere  strength. 

In  designing  the  floors  of  office  or  buildings  of  like  char¬ 
acter,  it  is  good  practice  to  figure  the  full  live  load  on  the  floor 
joists  or  beams,  but  to  consider  only  a  certain  percentage  as 
coming  upon  the  girders,  columns,  and  foundations,  on  the 
assumption  that  all  of  the  floors  will  not  be  fully  loaded  at  the 
same  time.  This  percentage  should  be  carefully  considered 
in  each  case  ;  and  the  amounts  will  depend  upon  the  height 
of  the  building  in  question  and  the  judgment  of  the  designer. 

In  proportioning  the  foundations  of  hotels,  office  buildings, 
etc.,  the  live  load  may  be  neglected,  but  should  be  considered 
in  heavy  warehouses.  In  buildings  carrying  heavy  machin¬ 
ery  causing  much  vibration,  it  is  good  practice  to  double  the 
estimated  live  load. 


LOADS  ON  STRUCTURES. 


67 


SNOW  AND  WIND  LOADS. 

Data  in  regard  to  snow  and  wind  loads  are  necessary  in 
connection  with  the  design  of  roof  trusses. 

Snow  Load.-— When  the  slope  of  a  roof  is  over  12  in.  rise  per 
foot  of  horizontal  run,  a  snow  and  accidental  load  of  8  lb.  per 
sq.  ft.  is  ample.  When  the  slope  is  under  12  in.-rise  per  foot 
of  run,  a  snow  and  accidental  load  of  12  lb.  per  sq.  ft.  should 
be  used.  The  snow  load  acts  vertically,  and  therefore  should 
be  added  to  the  dead  load  in  designing  roof  trusses.  The 
snow  load  may  be  neglected  when  a  high  wind  pressure  has 
been  considered,  as  a  great  wind  storm  would  very  likely 
remove  all  the  snow  from  the  roof. 

Wind  Load. — The  wind  is  considered  as  blowing  in  a  hori¬ 
zontal  direction,  but  the  resulting  pressure  upon  the  roof  is 
always  taken  normal  (at  right  angles)  to  the  slope.  The  wind 
pressure  against  a  vertical  plane  depends  on  the  velocity  of 
the  wind,  and,  as  ascertained  by  the  U.  S.  Signal  Service  at 
Mt.  Washington,  N.  H.,  is  as  follows: 


TABLE  VI. 


Velocity. 

Pressure. 

(Mi.  per  Hr.) 

(Lb.  per  Sq.  Ft.) 

10 . 

.  0.4 . 

. Fresh  breeze. 

20 . 

.  1.6 . 

. Stiff  breeze. 

30 . 

.  3.6 . 

....Strong  wind. 

40 . 

.  6.4 . 

....  High  wind. 

50 . 

. 10.0 . 

. Storm. 

60 . 

. 14.4 . 

. Violent  storm. 

80 . 

. 25.6 . 

. Hurricane. 

100 . 

. 40.0 . 

...  Violent  hurricane. 

The  wind  pressure  upon  a  cylindrical  surface  is  one-half 
that  upon  a  flat  surface  of  the  same  height  and  width. 

Since  the  wind  is  considered  as  traveling  in  a  horizontal 
direction,  it  is  evident  that  the  more  nearly  vertical  the  slope 
of  the  roof,  the  greater  will  be  the  pressure,  and  the  more 
nearly  horizontal  the  slope,  the  less  will  be  the  pressure. 
Table  VII  gives  the  pressure  exerted  upon  roofs  of  different 
slopes,  by  a  wind  pressure  of  40  lb.  per  sq.  ft.  on  a  vertical 
plane,  which  is  equivalent  in  intensity  to  a  violent  hurricane, 


68 


STRUCTURAL  DESIGN. 


TABLE  VII. 

Wind  Pressure  on  Roofs. 
Pounds  per  Square  Foot. 


Rise. 

In.  per 
Foot  of  Run. 

Angle 

With 

Horizontal. 

Pitch. 

Proportion  of 
Rise  to  Span. 

Wind  Pressure 
Normal 
to  Slope. 

4 

18°  25' 

h 

16.8 

6 

26°  33' 

I 

23.7 

8 

33°  41' 

1 

3 

i 

29.1 

12 

45°  O' 

36.1 

16 

53°  7' 

1 

38.7 

18 

56°  20' 

i 

39.3 

24 

63°  27' 

1 

40.0 

In  addition  to  wind  and  snow  loads  upon  roofs,  the  weight 
of  the  principals  or  roof  trusses,  including  the  other  features 
of  the  construction,  should  be  figured  in  the  estimate.  For 
light  roofs  having  a  span  of  not  over  50  ft.,  and  not  required 
to  support  any  ceiling,  the  weight  of  the  steel  construction 
may  be  taken  at  5  lb.  per  sq.  ft. ;  for  greater  spans,  1  lb.  pel 
sq.  ft.  should  be  added  for  each  10  ft.  increase  in  the  span. 


STRENGTH  OF  MATERIALS. 


DEFINITIONS  OF  TERMS. 

Stress. — This  is  the  cohesive  force  by  which  the  particles  of 
a  body  resist  the  external  load  that  tends  to  produce  an  altera¬ 
tion  in  the  form  of  the  body.  Stress  is  always  equal  to  the 
effective  external  force  acting  upon  the  body ;  thus,  a  bar 
subjected  to  a  direct  pulling  force  of  1,000  lb.  endures  a  stress 
of  1,000  lb.  Unit  stress  is  the  stress  or  load  per  square  inch  of 
section.  For  instance,  if  the  bar  mentioned  above  is  1  in. 
X  2  in.  in  section,  the  unit  stress  of  the  bar  would  be  1,000  lb. 
-v-2sq.  in.  (sectional  area)  =  5001b. 

Tensile  stress  is  produced  when  the  external  forces  tend  to 
Stretch  9  body,  or  pull  the  particles  away  from  one  another. 


STRENGTH  OF  MATERIALS. 


61* 


A  rope  by  which  a  weight  is  suspended  is  an  example  of  a. 
body  subjected  to  tensile  stress.  Compressive  stress  is  produced 
when  the  forces  tend  to  compress  the  body,  or  push  the  par¬ 
ticles  closer  together.  A  post  or  column  of  a  building  is  sub¬ 
jected  to  compressive  stress.  Shearing  stress  is  produced  when 
the  forces  tend  to  cause  the  particles  in  one  section  of  a  body 
to  slide  over  those  of  the  adjacent  section.  A  steel  plate 
acted  on  by  the  knives  of  a  shear,  or  a  beam  carrying  a  load, 
are  subjected  to  shearing  stress.  Transverse  or  bending  stress 
is  produced  by  loads  acting  on  a  beam  tending  to  bend  it, 
and  is  a  combination  of  tensile,  compressive,  and  shearing 
stresses. 

The  ultimate  strength  of  any  material  is  that  unit  stress 
which  is  just  sufficient  to  break  it.  The  ultimate  elongation  is 
the  total  elongation  produced  in  a  unit  of  length  of  the 
material  of  a  unit  area,  by  a  stress  equal  to  the  ultimate 
strength  of  the  material. 

Strain. — The  amount  of  alteration  in  form  of  a  body  pro¬ 
duced  by  a  stress  is  called  strain.  If  a  steel  wire  is  subjected 
to  a  pulling  stress,  and  is  elongated  of  an  in.,  this  alteration 
is  the  strain.  Unit  strain  is  the  strain  per  unit  of  length  or  of 
area.  It  is  usually  taken  per  unit  of  length,  and  is  called  the 
elongation  per  unit  of  length.  If  an  iron  bar  6  ft.  long  is  sub¬ 
jected  to  a  pulling  or  tensile  force  which  elongates  it  1  in., 
the  unit  strain  will  be  1  in.  -r-  72  (length  of  the  bar  in  inches) 
=  .0139  in. 

Modulus  of  Elasticity. — The  modulus  or  coefficient  of  elasticity 
is  the  ratio  between  the  stresses  and  corresponding  strains 
for  a  given  material,  which  may  have  a  somewhat  different 
modulus  of  elasticity  for  tension,  compression,  and  shear.  If  l 
be  the  strain  or  increase  per  unit  length  of  a  material  subjected 
to  tensile  stress,  and  p  the  unit  stress  producing  this  elonga- 

tion,  the  modulus  of  elasticity  E  —  -•  For  example,  a 


wrought-iron  bar,  80  in.  long,  subjected  to  a  unit  tensile 
stress  p  of  10,000  lb.,  stretched  .029  in.  The  unit  strain  l,  or 
stretch  per  inch  of  length,  is  .029  in.  -f-  80  in.  =  .0003625  in. 


Then, 


10,000 

,0003625 


27,586,200, 


70 


STRUCTURAL  DESIGN. 


The  relation  E  —  y  is  true  only  when  equal  additions  of 

stress  cause  equal  increases  of  strain.  Previous  to  rupture, 
this  condition  ceases  to  exist,  and  the  material  is  said  to  be 
strained  beyond  the  elastic  limit ,  which,  therefore,  is  that 
degree  of  stress  within  which  the  modulus  of  elasticity  is 
nearly  constant  and  equal  to  stress  divided  by  strain. 

Modulus  of  Rupture. — The  fibers  in  a  beam  subjected  to 
transverse  stresses  are  either  in  compression  or  tension, 
but  the  strength  of  the  extreme  fibers  agrees  neither  with 
their  compressive  nor  tensile  strength ;  hence,  in  beams  of 
uniform  cross-section  above  and  below  the  neutral  axis,  a 
constant  determined  by  actual  tests  is  used.  This  is  called 
the  modulus  of  rupture,  and  is  generally  expressed  in  pounds 
per  square  inch. 

Factor  of  Safety. — This  is  the  ratio  of  the  breaking  strength  of 
the  material  to  the  load  imposed  upon  it,  under  usual  condi¬ 
tions.  For  instance,  if  the  ultimate  strength  of  an  iron 
tension  bar  is  50,000  lb.,  and  the  load  it  sustains  is  10,000  lb., 
the  factor  of  safety  is  50,000  lb.  h-  10,000  lb.  —  5. 

TABLE  VIII. 


Strength  of  Metals  in  Pounds  per  Square  Inch. 


£5 

4-i 

4-1 

Material. 

o  . 

-+-•  O) 

s| 

<D  O 
■{j  *5q 

.§2 

2$ 

oS 

is 

°  a3 

Xfl  Sh 

3  2 

»-H  Q-3 

P  £< 

GO 

»i!d 
2  o  o 

*±  cu 
pH 

o 

cp 

'C  oSp 

—  E2^ 

f 

Wrought  iron . 

50,000 

44,000 

44,000 

48,000 

27 

Shape  iron  . 

48,000 

26 

Structural  steel . j 

60,000 

65,000 

52,000 

52,000 

60,000 

29 

Cast  iron  . 

18,000 

81,000 

25,000 

45,000 

12 

Steel,  castings  . 

70,000 

70,000 

60,000 

70,000 

30 

Brass,  cast  . 

24,000 

*30,000 

36,000 

20,000 

9 

Bronze,  phosphor . 

50,000 

14 

Bronze,  aluminum  . 

75,000 

120,000 

Aluminum,  commercial 

15,000 

12,000 

12,000 

11 

*  TJiiit  stress  producing  10^  reduction  in  original  length. 


TABLE  IX. 

Strength  of  Timber  in  Pounds  per  Square  Inch. 


STRENGTH  OF  MATERIALS. 


71 


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1,100,000 

1,000,000 

1,700,000 

1,400,000 

1,200,000 

1,200,000 

1,200,000 

1,400,000 

1,200,000 

900,000 

900,000 

700.000 

1,000,000 

700,000 

1,200,000 

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72 


STRUCTURAL  DESIGN. 


The  values  for  different  woods  in  Table  IX  are  aver¬ 
age  values  for  commercial  timber.  Column  3  in  the  table 
shows  the  ultimate  compressive  strength  parallel  to  the 

grain,  which  values  are  used  in 
figuring  the  ultimate  strength 
of  columns.  Column  4  gives 
the  allowable  compressive 
strength  perpendicular  to  the 
grain,  the  values  given  being 
the  load  per  square  inch  of 
section  required  to  produce  an 


Fig.  1. 


indenture  of  of  an  inch.  Reference  to  Fig.  1  will  explain 
this  more  clearly.  The  left-hand  portion  of  column  5  will  be 
found  of  use  in  calculating  the  resistance  of  the  timber  at  the 
heel  of  a  roof  truss.  For 
instance,  in  Fig.  2,  to 
calculate  with  what  force 
the  piece  c  of  the  tie 
member  b  opposes  the 
thrust  of  the  rafter  mem¬ 
ber  a.  The  sectional  area 
of  the  surface  dcf  is  10  in. 

X  18  in.  =  180  sq.  in.  The  ultimate  shearing  strength  of 
Georgia  yellow  pine,  parallel  with  the  grain,  according  to 
Table  IX,  is  600  lb.;  then,  180  X  600  =  108,000  lb.,  the  ultimate 
strength  of  the  timber.  If  the  safe  strength  is  desired,  divide 
by  the  required  factor  of  safety  ;  if  4  is  used  the  safe  strength 
will  be  108,000  -i-  4  =  27,000  lb.  Column  6,  giving  the  modulus 
of  rupture  for  different  woods,  is  used  in  figuring  the 
strength  of  beams  (see  page  106). 

From  recent  tests  to  determine  the  physical  properties  of 
timber,  made  by  the  Forestry  Division  U.  S.  Dept,  of  Agri¬ 
culture,  the  following  conclusions  are  deduced :  That  the 
bleeding  of  long-leaf  yellow  pine,  for  sap  products,  is  not 
detrimental  to  its  durability  and  strength ;  that  moisture 
reduces  the  strength  of  timber,  whether  that  moisture  be  the 
sap  or  that  absorbed  after  seasoning ;  also,  that  large  timbers 
are  equal  in  strength  to  small,  provided  they  are  sound  and 
contain  the  same  percentage  of  moisture. 


STRENGTH  OF  MATERIALS. 


73 


TABLE  X. 

Average  Ultimate  Strength  of  Masonry  Materials. 


Material. 

Compression. 

Lb.  per  Sq.  In. 

Tension. 

Lb.  per  Sq.  In. 

Modulus  of 

Rupture. 

Building  Stone. 

Bluestone . 

13,500 

1,400 

2,700 

Granite,  average . 

Connecticut . 

15,000 

12,000 

600 

1,800 

New  Hampshire . 

15,000 

1,500 

Massachusetts . 

New  York . 

16,000 

15,000 

1,800 

Limestone,  average  . 

Hudson  River,  N.  Y . 

7,000 

17,000 

1,000 

1,500 

Ohio . 

12,000 

1,500 

Marble,  Vermont  . 

8,000 

700 

1,200 

Sandstone,  average . 

5,000 

150 

1,200 

New  Jersey  . 

12,000 

650 

New  York . 

10,000 

1,700 

Ohio. . . 

9,000 

100 

700 

Slate . 

10,000 

4,000 

5,000 

Stonework  (strength  of  stone)  . 

4 

TS 

4 

1T5 

TS 

Brick. 

40 

Brick,  light  red . 

1,000 

600 

Good  common . 

10,000 

200 

Best  hard . 

12,000 

400 

800 

Philadelphia  pressed  . 

6,000 

200 

600 

Brickwork,  common  lime  mortar 

1,000 

50 

Good  cement-and-lime  mortar . 

1,500 

100 

Best  cement  mortar . 

Terra  cotta  . 

Terra-cotta  work' . 

2,000 

5,000 

2,000 

300 

Cements,  etc. 

200 

200 

Cement,  Rosendale,  1  mo.  old . 

1,200 

Portland,  1  mo.  old  . 

2,000 

400 

400 

Rosendale,  1  yr.  old . 

2,000 

300 

400 

Portland,  1  yr.  old . 

3,000 

500 

800 

Mortar,  lime,  1  yr.  old . 

400 

50 

100 

Lime  and  Rosendale,  1  yr.  old . 

600 

75 

200 

Rosendale  cement,  1  yr.  old . 

1,000 

125 

300 

Portland  cement,  1  yr.  old . 

2,000 

250 

600 

Concrete,  Portland,  1  mo.  old . 

1,000 

200 

100 

Rosendale,  1  mo.  old . 

500 

100 

50 

Portland,  1  vr.  old . 

2,000 

400 

150 

Rosendale,  1  yr.  old . 

1,000 

200 

75 

74 


STRUCTURAL  DESIGN. 


The  values  in  the  preceding  table  are  ultimate,  and  from 
ts  to  sV  of  these  values  is  used  as  the  safe  working  strength  of 
the  materials. 

The  following  table  gives  the  safe  working  loads  allowable 
in  good  practice  for  brickwork,  masonry,  and  foundation 
soils : 


TABLE  XI. 

Safe  Bearing  Loads. 


Brick  and  Stone  Masonry. 

Lb.  per 

Sq.  In. 

Brickwork. 

Bricks,  hard,  laid  in  lime  mortar  . 

100 

Hard,  laid  in  Portland  cement  mortar . 

200 

Hard,  laid  inRosendale  cement  mortar . 

150 

Masonry. 

Granite,  capstone . 

700 

Squared  stonework  . 

350 

Sandstone,  capstone . 

350 

Squared  stonework  . 

175 

Rubble  stonework,  laid  in  lime  mortar  . 

80 

Rubble  stonework,  laid  in  cement  mortar 

150 

Limestone,  capstone . 

500 

Squared  stonework  . 

250 

Rubbl$,  laid  in  lime  mortar . 

80 

Rubble,  laid  in  cement  mortar . 

150 

Concrete,  1  Portland,  2  sand,  5  broken  stone 

150 

Foundation  Soils. 


Tons 

per  Sq.  Ft. 


Rock,  hardest  in  native  bed . 

Equal  to  best  ashlar  masonry . 

Equal  to  best  brick  . 

Clay,  dry,  in  thick  beds . 

Moderately  dry,  in  thick  beds . 

Soft  . . 

Gravel  and  coarse  sand,  well  cemented 

Sand,  compact  and  well  cemented  . 

Clean,  dry . 

Quicksand,  alluvial  soils,  etc . 


100  — 
25—10 
15-20 
4-  6 
2-  4 
1-  2 
8-10 
4-  6 
2-  4 
.5-  1 


PROPERTIES  OF  SECTIONS. 


75 


PROPERTIES  OF  SECTIONS. 


CENTER  OF  GRAVITY. 

The  center  of  gravity  of  a  figure  or  body  is  that  point  upon 
Which  the  figure  or  body  will  balance  in  whatever  position 
it  may  be  placed,  provided  it  is  acted  upon  by  no  other  force 
than  gravity. 

If  a  plane  figure  is  alike  or  symmetrical  on  both  sides  of  a 
center  line,  the  latter  line  is  termed  an  axis  of  symmetry ,  and 
the  center  of  gravity  lies  in  this  line.  If  the  figure  is  symmet¬ 
rical  about  any  other  axis,  the  intersection  of  the  two  axes  will  he 
the  center  of  gravity  of  the  section.  Thus,  the  center  of  gravity 
of  a  square,  rectangle,  or  other  parallelogram  is  at  the  inter¬ 
section  of  the  diagonals ;  of  a  circle  or  ellipse,  at  the  center 
of  figure ;  etc.  The  center  of  gravity  of  a  triangle  is  found  at 
the  intersection  of  lines  drawn  from  the  middle  of  each  side 
to  the  opposite  apex  ;  or,  it  is  §  the  distance  from  any  apex 
to  the  middle  of  the  opposite  side.  For  any  section,  the 
center  of  gravity  may  be  found  by  the  principles  explained 
in  the  following  article  on  Neutral  Axis.  It  may  be  deter¬ 
mined  approximately,  but  simply,  by  drawing  to  scale  upon 
cardboard  the  outline  of  the  section  ;  then,  by  cutting  out  the 
figure,  and  balancing  it  in  different  directions  on  a  knife 
edge,  the  center  of  gravity  will  be  at  the  intersection  of  the 
lines  on  which  the  section  balances. 


NEUTRAL  AXIS., 

When  a  simple  beam  is  loaded,  there  is  always  compres¬ 
sion  in  the  topmost  fibers  and  tension  in  the  bottommost 
fibers.  There  must,  therefore,  be  a  certain  position  in  the 
cross-section  at  which  the  fibers  are  neither  in  compression 
nor  tension — that  is,  they  are  neutral;  hence  the  position  of 
these  neutral  fibers  is  called  the  neutral  axis  of  the  section. 
The  neutral  axis  of  a  beam  section  passes  through  the  center 
of  graxnty  of  the  section,  and  at  right  angles  to  the  direction 
in  which  the  loads  act.  If  the  section  of  the  beam  is  sym¬ 
metrical  its  axis  of  symmetry  will  be  a  neutral  axis,  provided 


76 


STRUCTURAL  DESIGN. 


it  is  "perpendicular  to  the  line  of  action  of  the  loads.  By 
finding  the  center  of  gravity  of  a  cardboard  pattern,  the 
neutral  axis  of  any  section  may  be  located. 

For  simple  sections,  such  as  rect¬ 
angles,  triangles,  etc.,  the  required 
neutral  axis  is  found  by  the  fore¬ 
going  principles.  When,  however, 
the  section  is  made  up  of  combi¬ 
nations  of  rectangles,  etc.,  as  in 
Fig.  3,  the  distance  c  of  the  neutral 
axis  from  any  line  or  origin  of 
moments  (usually  taken  at  an 
edge  of  the  section)  may  be  cal¬ 
culated  as  follows : 

Rule. — Find  the  sum  of  the  products  of  the  area  of  each 
elementary  section  multiplied  by  the  perpendicular  distance 
between  its  center  of  gravity  and  the  line  or  origin  of  moments; 
divide  this  sum  by  the  total  area  of  the  figure;  the  result  will  give 
the  required  distance  c. 

Example. — The  distance  c,  in  Fig.  4,  is  thus  found;  the  line 
»r  origin  of  moments  being  taken  at  the  line  a  b : 


;j 


1 

2 

3 

4 

5 

Elementary 

Section. 

Dimensions. 

Inches. 

Area. 
Sq.  In. 

Distance 
From  a  b 
to  Center 
of 

Gravity. 

Inches. 

Prod¬ 
ucts. 
Col.  3  X 
Col.  4. 

Upper  plate  . 

2  upper  angles— 

Web-plate . 

2  lower  angles... 
Lower  plate . 

8"  X 

*  3"  X  3"  X  f" 
18"  X  ¥' 

3  h"  X  3i"  X  i" 
12"  X  i" 

4.00 

3.56  X  2 
9.00 

3.98  X  2 
6.00 

.25 
f  1.53 
9.50 
17.40 
18.75 

1.00 

10.89 

85.50 

138.50 

112.50 

Totals  . 

34.08 

348.39 

,  *  For  areas,  see4able,  page  85.  For  decimal  equivalents  of 

fractions  of  inches,  see  page  53.  f  See  table,  page  85. 


PROPERTIES  OF  SECTIONS. 


77 


Therefore,  distance  c  of  neutral 
axis  (and  center  of  gravity)  from 
ab  =  348.39 -T- 34.08  =  10.22  in. 


By  finding  another  neutral  axis 
in  similar  manner,  the  intersection 
of  the  two  axes  will  be  the  center 
of  gravity  of  the  section.  If  the 
section,  as  in  Fig.  4,  is  symmetrical 
about  a  vertical  axis,  the  intersec¬ 
tion  of  this  axis  and  the  neutral 
axis  will  be  the  center  of  gravity. 


J 


I  i  , 

y/t% 


Fig.  4. 


MOMENT  OF  INERTIA 


When  a  beam  is  subjected  to  loading,  as  in  Fig.  5,  the 
fibers  of  the  beam  tend  to  resist  the  compression  at  the  top 
and  the  tension  at  the  bottom,  each  fiber  exerting  a  force  or 


moment  directly 
proportional  to  the 
distance  it  is 
located  from  the 
neutral  axis  (pro* 
vided  the  elastic 
limit  of  the  mate¬ 
rial  is  not  ex- 


Support 


Support 


Fig.  5. 


ceeded) ;  hence,  the  topmost  and  bottommost  fibers  are  of 
considerably  more  value  than  those  located  near  the  neutral 
axis.  It  is  therefore  necessary,  before  the  strength  of  any 
section  can  be  obtained,  to  ascertain  the  average  value  of  all 
the  fibers  in  the  section ;  this  value  is  called  the  moment  of 
inertia. 

The  moment  of  inertia  (usually  designated  by  the  letter  I) 
of  any  body  or  figure  is  the  sum  of  the  products  of  each 
particle  of  the  body  or  elementary  area  of  the  figure  multi¬ 
plied  by  the  square  of  its  distance  from  the  axis  around 
which  the  body  would  rotate.  This  axis  is  the  neutral  axis. 

For  example,  assuming  that  the  section  shown  in  Fig.  6 
is  3  in.  X  12  in.,  and  that  it  is  divided  into  36  equal  parts,  each 
having  an  area  of  1  sq.  in.,  the  approximate  moment  of 
inertia  may  be  calculated  as  follows: 


78 


STRUCTURAL  DESIGN. 


Fibers  b,  b,  b,  b,  b,  b 
Fibers  c,  c,  c,  c,  c,  c 
Fibers  d,  d,  d,  d,  d,  d 
Fibers  e,  e,  e,  e,  e,  e 
Fibers  /,  /,  /,  /,  /,  / 
Fibers  g,  g,  g,  g,  g,  g 


6  sq.  in.  X  5.5  X  5.5  —  181.50 

6  sq.  in.  X  4.5  X  4.5  =  121.50 

6  sq.  in.  X  3.5  X  3.5  =  73.50 

6  sq.  in.  X  2.5  X  2.5  =  37.50 

6  sq.  in.  X  1.5  X  1.5  =  13.50 

6  sq.  in.  X  .5  X  .5  =  1.50 


.1; 


I,  or  moment  of  inertia  =  429.00 

In  this  manner  the  approximate  moment  of  inertia  for 
any  section  may  be  obtained.  Table  XII,  page  83,  gives  con¬ 
venient  formulas  by  which 
the  moment  of  inertia  for 
usual  sections  may  be  de¬ 
termined.  For  instance, 
according  to  this  table,  the 
formula  for  the  moment  of 
inertia  of  any  rectangular 

section  is  I  —  in  which 

b  is  the  breadth  of  the 
beam,  and  d  the  depth. 
Thus,  the  moment  of  inertia  for  the 
section  shown  in  Fig.  6  may  be  found 
as  follows : 

y  3  x  12  X  12  X 12 


b 

b 

b- 

c 

c 

c- 

d 

a 

A  - 

e 

c 

e — 

f 

t 

/- 

a 

a 

9— 

V 

a 

V 

f 

f 

f 

C 

e 

e 

d 

<1 

A 

c 

c 

c 

V 

b 

—  i  **  I 


«5 

>0 


La 


12 


432, 


Fig.  6. 


which  is  nearly  the  same  as  the  approxi¬ 
mate  result,  429,  obtained  in  the  previous 
calculation. 

Tables  XIII  to  XIX,  on  pages  84  to  90, 
give  the  moment  of  inertia  for  rolled 
steel  sections,  and  will  be  found  useful  in  designing  structural 
steel  work. 

As  beam  or  column  sections  are  often  made  up  of  several 
elementary  sections,  the  moment  of  inertia  is  then  found  thus : 

Rule. —  The  moment  of  inertia  is  equal  to  the  sum  of  the  prod¬ 
ucts  of  each  elementary  area  multiplied  by  the  square  of  its 
distance  from  the  neutral  axis,  plus  its  moment  of  inertia  about 
a  parallel  axis  through  its  center  of  gravity. 


PROPERTIES  OF  SECTIONS. 


79 


a/8  P/afe 


If  i  represents  the  moment  of  inertia  of  each  elementary 
figure,  a  the  area  of  each,  d 2  the  square  of  the  perpendicular 
distance  from  the  center  of  gravity  of  each  elementary 
section  to  the  neutral  axis  a  6,  Fig.  7, 
and  I  the  required  moment  of  iner¬ 
tia,  the  rule  may  be  expressed  thus : 

1=  2  (ad2  +  i). 

Example. — The  moment  of  iner¬ 
tia  of  the  section  shown  in  Fig.  4 
may  he  found  as  follows,  the  figure 
being  redrawn  with  the  neutral  axis 
located  by  the  distance  c,  obtained 
from  calculations  on  page  77,  and 
shown  in  Fig.  7. 

Solution. — First  work  out  the  for-  Fig.  7. 

mula  ad'2  +  i  for  each  elementary  section,  as  in  the  follow¬ 
ing  table. 


T 

3X3X§ id 
% 
I 

iX/8P/atl 


\3£3£rf\ii 
£X/2pZfe 


Elementary 

Section. 

Area  a. 
Sq.  In. 

d. 

In. 

dK 

i. 

ad-  +  i. 

Upper  plate  . 

4.00 

9.97 

99.4 

*.0833 

397.68 

2  upper  angles . 

f3.56X2 

8.69 

75.51 

13.20X2 

544.03 

Web-plate  . 

9.00 

.72 

.5184 

243.00 

247.66 

2  lower  angles . 

3.98X2 

7.18 

51.55 

4.33X2 

418.99 

Lower  plate  . . . 

6.00 

8.53 

72.76 

.125 

436.68 

Moment  of  inertia  of  section,  I  =  2  (a  d-  +  i)  =  2,015.04. 

Graphical  Method. — The  location  of  the  neutral  axis  and  the 
moment  of  inertia  of  any  section  may  be  obtained  by  the 
following  graphical  method,  which  is  sufficiently  accurate  for 
all  practical  purposes. 

Example. — Locate  the  neutral  axis,  and  find  the  moment 
of  inertia  of  the  section  shown  at  (a) ,  Fig.  8. 

Solution.— First,  draw  the  section,  either  full  size  or  to 
any  scale,  as  at  (a). 


*  Figured  by  formula  -vx- ,  on  page  83.  f  See  page  85, 


80 


STRUCTURAL  DESIGN. 


Second ,  divide  this  section  by  horizontal  lines  into  strips  of 
equal  or  unequal  height ;  find  the  area  in  square  inches  and 
the  center  of  gravity  of  each  strip ;  since  the  strips  in  this 
case  are  rectangles,  the  centers  of  gravity  will  be  at  the  cen¬ 
ters  of  the  strips,  through  which  points  dot-and-dash  lines 
have  been  drawn. 

Third,  on  any  horizontal  line  lay  off,  from  left  to  right, 
to  any  scale,  distances  proportional  to  the  area  of  the  strips, 
talcing  them  in  order  from  top  to  bottom  of  the  section.  This 
horizontal  line  may  be  called  the  load  or  area  line.  Thus, 
at  (b) ,  the  distances  A  B,  B  C,  CD,  etc.  are  measured  to  a  scale 
of,  say,  in.  to  1  sq.  in.  area,  and  represent  the  areas  of  the 
sections  P,  Q,  R,  etc.,  respectively,  in  (a). 


Fourth,  from  the  ends  A  and  M  of  this  line,  draw  lines 
inclined  45°  to  it,  and  intersecting  at  a  point  N  called  the 
pole.  Draw  lines  from  N  to  points  B,  C,  D,  etc. 

Fifth,  commencing  anywhere  on  a  horizontal  line  through 
the  top  of  the  section,  draw  the  line  1-2  parallel  with  the  45°  line 
A  N ;  from  the  intersection  of  this  line  with  one  through  the 
center  of  gravity  of  slice  P,  draw  2-3  parallel  with  B  N ;  from 
the  intersection  of  2-3  with  the  horizontal  line  passing  through 
the  center  of  gravity  of  slice  Q,  draw  the  line  3- 4  parallel  to 
CN.  Continue  in  this  manner,  drawing  the  remaining 
lines  A-5,  5-6,  etc.,  parallel,  respectively,  to  DN,  EN,  etc. 

Sixth,  draw,  from  the  points  1  and  11  at  the  end  of  the 
curve,  45°  lines  intersecting  at  the  point  12,  through  which 


PROPERTIES  OF  SECTIONS.  81 

draw  a  horizontal  line,  cutting  the  section  as  shown  at  (a), 
Fig.  8 ;  this  line  will  he  the  neutral  axis  of  the  figure. 

Seventh,  the  moment  of  inertia  I  may  he  found  hy  multi¬ 
plying  the  area  *  in  square  inches  of  the  section-lined  figure 
by  the  entire  area  of  the  section.  Thus,  if  in  this  case  the 
area  of  the  former  is  4.67  sq.  in.,  and  that  of  the  section  at  (a) 
is  16.25  sq.  in.,  the  moment  of  inertia  will  be  equal  to  16.25  sq. 
in.  X  4.67  sq.  in.  =  75.88,  the  value  of  I  for  this  section. 


RADIUS  OF  GYRATION. 


This  term,  like  moment  of  inertia,  is  the  expression  of  a 
certain  value  ot  any  section,  and  is  one  of  the  factors  in  the 
principal  column  formulas  for  determining  the  strength  of 
cast-iron  and  steel  columns. 

Rule. — The  radius  of  gyration  ( R )  of  any  section  is  equal  to 
the  square  root  of  the  quotient  obtained  by  dividing  the  moment 
of  inertia f  of  the  section  (I)  by  the  area  of  the  section  {A). 

The  rule  may  be  thus  expressed  by  formula : 


R 


For  convenient  formulas  to  obtain  the 
radius  of  gyration  of  usual  sections,  see 
Table  XII,  page  83.  For  the  radius  of 
gyration  of  rolled  shapes,  see  tables  on 
pages  84  to  93. 

Example.— What  is  the  least  radius 
of  gyration  of  the  structural  steel- 
column  section  shown  in  Fig.  9? 

Solution.— The  value  of  J,  or  moment 
of  inertia  (found  by  one  of  the  methods 
given  on  pages  78  to  80),  on  the  axis  XX,  is 
while  on  the  axis  Y  Y  it  is  equal  to  366.1. 
area  is  41.44  sq.  in.  Using  the  least  value  of  I, 

R  =  a  ! 55,  or  2.97. 


Fig.  9. 

equal  to  1,129, 
The  sectional 
there  results, 


41.44’ 


*To  find  area  of  irregular  figures,  see  page  36.  In  obtain¬ 
ing  dimensions  necessary  for  determining^  the  area,  the 
same  scale  should  be  adopted  as  used  in  laying  out  the  sec¬ 
tion  at  (a),  Fig.  8.  f  See  pages  77  to  81. 


82 


STRUCTURAL  DESIGN. 


SECTION  MODULUS,  OR  RESISTING  INCHES. 


The  section  modulus ,  or,  as  it  is  sometimes  called,  resisting 
inches,  of  a  section  is  equal  to  the  moment  of  inertia  divided  by 
the  greatest  distance  of  the  neutral  axis  from  the  outside  fibers 
of  the  figure  or  section.  This  rule  expressed  in  formula 
would  be, 


where,  Q  —  section  modulus ; 

I  —  moment  of  inertia  *  of  the  section  ; 

c  =  greatest  distance  from  the  outside  fiber 
to  the  neutral  axis  f . 

Example. — What  is  the  section  modulus  for  the  cross-sec¬ 
tion  of  a  3"  X  12"  joist  ? 

Solution. — Since  the  cross-section  is  rectangular,  the 
neutral  axis  must  pass  through  the  center  of  the  section, 
and  the  distance  c  is  in  this  case  equal  to  one-half  the  depth, 
that  is,  6  in.  The  moment  of  inertia  may  be  found  by  the 
method  given  on  page  77  ;  or  more  easily  by  the  formula  for 
rectangular  sections  given  in  Table  XII,  on  page  83.  This 
bd 3 

formula  is  I  —  — - -,  where  b  =  the  breadth,  and  d  =  the  depth 

JLZ 


of  the  joist. 
Then, 


I  = 


3  X  12  X  12  X  12 
12 


or  432. 


Having  found  the  value  of  c  and  I,  they  may  be  substi¬ 
tuted  in  the  formula  for  obtaining  the  section  modulus,  and 


which  is  the  section  modulus,  or  resisting  inches,  for  a 
3"  X  12"  joist. 

Formulas  for  obtaining  directly  the  section  modulus  of 
the  usual  sections  are  given  in  Table  XII,  page  83.  The  section 
modulus  is  given  for  the  usual  rolled  structural  sections  in 
the  tables  on  pages  84  to  90. 

These  latter  are  especially  convenient  as  by  them  sections 
of  different  dimensions  can  be  readily  compared,  and  the 
most  economical  selected. 


*  See  page  77.  f  See  page  76. 


PROPERTIES  OF  SECTIONS. 


83 


TABLE  XII. 


Shape 

of 

Section. 


Moment 

of 

Inertia. 

I. 

Section 

Modulus. 

Q- 

Sq.  Least 
Radius  of 
Gyration. 
R2. 

d 4 

d3 

d2 

12 

6 

12 

bd3 

bd2 

62 

12 

6 

12 

6 4  -  b '4 

I 

&2  -f&'2 

12 

.56 

12 

b  d3  —  b' d'3 

I 

I 

12 

.5  d 

A 

7T  1 4 

“  ,  or  .0491  d4 
64 

IT 

— — ,  or  .0982  ds 

oA 

d2 

16 

.0491  (d4  -  d'4) 

/7/4\ 

.0982(d3 - ^  » 

d2+d'2 

16 

&  d3  _  2  6' d'3 

I 

I 

12 

0.5  d 

A 

^  (Approx.) 
0.00 

(Approx.) 

I 

A 

A  (72 

(Approx.) 

^J<Approx-> 

I 

A 

Note  —  4.  =  total  area  of  section.  In  calculating  the  least 
radius  of  gyration  be  sure  to  use  the  least  moment  of  inertia. 
xx'  denotes  the  neutral  axis,  and  the  value  of  I  given  is  that 
about  this  axis, 


84 


STRUCTURAL  DESIGN. 


TABLE  XIII. 

Properties  of  Steel  Channels. 


Depth  of  Channel. 

Weight  per  Foot. 

Area. 

Thickness  of  Web. 

Width  of  Flange. 

Neutral  Axis 
Perpendicular  to 
Web  at  Center. 

Neutral  Axis 
Parallel  to  Back 
of  Channel. 

Moment  of  Inertia. 

Section  Modulus. 

Radius  of  Gyration. 
Inches. 

Moment  of  Inertia. 

Radius  of  Gyration. 

Inches. 

Center  of  Gravity 

From  Back. 

In. 

Lb. 

Sq.  In. 

In. 

In. 

I. 

Q. 

R. 

r. 

S'. 

In. 

15 

50 

14.71 

.72 

3.72 

402.70 

53.70 

5.23 

11.220 

.87 

.80 

15 

40 

11.80 

.47 

3.63 

371.60 

49.50 

5.62 

11.500 

.99 

.89 

15 

33 

9.70 

.40 

3.38 

304.20 

40.50 

5.64 

7.900 

.92 

.79 

12 

40 

11.76 

.76 

3.42 

197.00 

32.80 

4.09 

6.630 

.75 

.72 

12 

27 

7.90 

.38 

3.13 

161.00 

26.80 

4.54 

5.730 

.86 

.78 

12 

20 

5.90 

.28 

2.88 

124.70 

20.80 

4.59 

3.690 

.79 

.69 

10 

30 

8.82 

.68 

3.04 

103.20 

20.60 

3.42 

3.990 

.67 

.65 

10 

20 

5.90 

.31 

2.88 

85.50 

17.10 

3.81 

3.750 

.80 

.74 

10 

15 

4.40 

.25 

2.60 

66.82 

13.40 

3.89 

2.490 

.74 

.66 

9 

16 

4.70 

.28 

2.56 

57.09 

12.70 

3.48 

2.590 

.74 

.66 

9 

13 

3.80 

.23 

2.36 

45.48 

10.10 

3.46 

1.640 

.64 

.57 

8 

13 

3.80 

.25 

2.22 

35.56 

8.89 

3.07 

1.470 

.62 

.58 

8 

10 

3.00 

.20 

2.08 

28.20 

7.05 

3.08 

1.000 

.58 

.52 

7 

13 

3.80 

.28 

2.22 

27.35 

7.81 

2.69 

1.890 

.71 

.62 

7 

9 

2.61 

.20 

2.00 

19.05 

5.43 

2.70 

.814 

.56 

.51 

6 

17 

4.85 

.38 

2.41 

25.43 

8.48 

2.28 

2.390 

.70 

.78 

6 

12 

3.48 

.28 

2.19 

18.70 

6.23 

2.32 

1.380 

.63 

.65 

6 

8 

2.35 

.20 

1.94 

12.75 

4.25 

2.33 

.710 

.55 

.52 

5 

9 

2.59 

.25 

1.91 

9.67 

3.87 

1.93 

.810 

.55 

.57 

5 

6 

1.76 

.18 

1.66 

6.53 

2.61 

1.93 

.390 

.47 

.45 

4 

8 

2.31 

.27 

1.86 

5.47 

2.73 

1.54 

.685 

.55 

.59 

4 

5 

1.46 

.17 

1.59 

3.59 

1.80 

1.57 

.293 

.45 

.46 

3 

6 

1.76 

.36 

1.60 

2.10 

1.40 

1.08 

.310 

.42 

.46 

3 

5 

1.47 

.26 

1.50 

1.80 

1.20 

1.12 

.250 

.41 

.44 

3 

4 

1.19 

.17 

1.41 

1.60 

1.10 

1.17 

.200 

.41 

.44 

PROPERTIES  OF  SECTIONS. 


85 


TABLE  XIV. 

Properties  op  Steel  Angles— Equal  Legs. 


Size  of  Angles. 

Thickness. 

Weight  per  Foot. 

Area  of  Section. 

Distance  from  Cen¬ 
ter  of  Gravity  to 
Back  of  Flange. 

Moment  of  Inertia, 

Axis  Parallel  to 

Flange. 

Section  Modulus, 

Axis  as  Before. 

Radius  of  Gyration, 

Axis  as  Before. 

In. 

In. 

Lb. 

Sq.  In. 

In. 

I. 

Q. 

R. 

6  X  6 

_7 

34.00 

10.03 

1.87 

35.300 

8.170 

1.87 

6  X  6 

7 

17.20 

5.06 

1.66 

17.680 

4.070 

1.87 

6  X6 

3. 

14.80 

4.36 

1.64 

15.400 

3.520 

1.88 

5  X  5 

f 

24.20 

7.11 

1.56 

17.000 

4.780 

1.55 

5  X5 

i 

12.30 

3.61 

1.39 

8.740 

2.420 

1.56 

4  X  4 

1  3 

1 

20.80 

6.11 

1.35 

9.450 

3.320 

1.24 

4  X  4 

5 

1(5 

8.16 

2.40 

1.12 

3.720 

1.290 

1.24 

3£X3i 

1 

13.50 

3.98 

1.10 

4.330 

1.810 

1.04 

3£X3i 

7.11 

2.09 

.99 

2.450 

.9S0 

1.08 

3  X  3 

12.10 

3.56 

1.03 

3.200 

1.480 

.94 

3  X  3 

i 

4.90 

1.44 

.84 

1.240 

.580 

.93 

2£X2i 

1 

7.85 

2.31 

.82 

1.330 

.760 

.76 

2£X2i 

l. 

4.05 

1.19 

.72 

.700 

.400 

.77 

2iX2i 

1 

7.17 

2.11 

.78 

1.040 

.650 

.70 

2iX2| 

X 

3.70 

1.06 

.66 

.510 

.320 

.69 

2iX2i 

A 

2.75 

.81 

.63 

.390 

.240 

.69 

2  X  2 

i 

6.32 

1.86 

.72 

.720 

.510 

.62 

2  X  2 

2.41 

.71 

.57 

.280 

.190 

.62 

If  XU 

TB 

4.72 

1.39 

.61 

.390 

.320 

.52 

If  Xlf 

A 

2.11 

.62 

.51 

.180 

.140 

.54 

UXli 

t 

3.33 

.98 

.51 

.190 

.190 

.44 

HXU 

1.80 

.53 

.44 

.110 

.104 

.46 

U  X  if 

5 

TB 

2.55 

.75 

.46 

.123 

.134 

.40 

UXH 

1.02 

.30 

.35 

.044 

.049 

.38 

1  XI 

1 

1.57 

.46 

.36  . 

.045 

.064 

.31 

1  XI 

i. 

.78 

.23 

.30 

.022 

.031 

.31 

2.  N/  1 

3 

Tff 

.99 

.29 

.29 

.019 

.033 

.26 

7  W  7 

•g*  A  ■§■ 

.68 

.20 

.25 

.014 

.022 

.27 

fX  f 

3 

.85 

.25 

.26 

.012 

.024 

.22 

fX  f 

8 

.58 

.17 

.23 

.009 

.017 

.23 

86 


STRUCTURAL  DESIGN. 


TABLE  XV. 

Properties  of  Steel  Angles— Unequal  Legs. 


Size  of  Angle. 

Weight  per  Foot 

Area  of  Section. 

Neutral  Axis 
Parallel  to 
Shorter  Flange. 

Neutral  Axis 
Parallel  to 
Longer  Flange. 

Center  of  Gravity.* 

Moment  of  Inertia. 

Section  Modulus. 

Kad.  of  Gyration.  (In.) 

Center  of  Gravity.* 

Moment  of  Inertia. 

Section  Modulus. 

d 

t— i 

d 

o 

•i-H 

c3 

o 

o 

'd 

aj 

PS 

Inches. 

Lb. 

Sq. 

In. 

In. 

I. 

Q- 

R. 

In. 

r. 

Q'. 

R' 

6X4X1 

28.4 

8.34 

2.2 

31.84 

7.89 

1.9 

1.18 

11.81 

3.85 

1.2 

6X4X1 

12.3 

3.61 

1.9 

13.51 

3.32 

1.9 

.94 

4.90 

1.60 

1.2 

5  X  31 X  i 

20.3 

5.98 

1.8 

15.15 

4.53 

1.6 

1.03 

6.23 

2.39 

1.0 

5  X3iX  % 

10.4 

3.05 

1.6 

7.78 

2.29 

1.6 

.86 

3.18 

1.21 

1.0 

5X3X1 

19.3 

5.68 

1.9 

14.91 

4.55 

1.6 

.88 

4.27 

1.85 

.9 

6  X  3  X  vb 

8.2 

2.40 

1.7 

6.26 

1.89 

1.6 

.68 

1.75 

.75 

.8 

41 X 3  Xi 

17.8 

5.23 

1.7 

10.73 

3.59 

1.4 

.91 

3.89 

1.75 

.9 

41X3  X ts 

7.7 

2.25 

1.5 

4.67 

1.54 

1.5 

.72 

1.70 

.75 

.9 

4  X  31 X  i 

17.8 

5.23 

1.4 

8.12 

2.95 

1.2 

1.12 

5.83 

2.33 

1.0 

4  X  31 X  ts 

7.7 

2.25 

1.2 

3.57 

1.24 

1.3 

.93 

2.55 

.99 

1.1 

4X3X1 

13.5 

3.98 

1.4 

6.04 

2.31 

1.2 

.87 

2.73 

1.28 

.8 

4  X  3  X  tb 

7.1 

2.09 

1.3 

3.38 

1.23 

1.3 

.76 

1.65 

.74 

.9 

31X3  XI 

12.5 

3.67 

1.2 

4.11 

1.76 

1.1 

.92 

2.75 

1.32 

.9 

31X3  Xtb 

6.6 

1.93 

1.1 

2.33 

.96 

1.1 

.81 

1.58 

.72 

.9 

31  X  21 X  t9b 

10.6 

3.13 

1.2 

3.76 

1.62 

1.1 

.75 

1.61 

.89 

.7 

31  X  21 X  i 

4.9 

1.44 

1.1 

1.80 

.75 

1.1 

.61 

.78 

.41 

.7 

3  X  21 X  tb 

9.7 

2.84 

1.0 

2.44 

1.21 

.9 

.79 

1.53 

.86 

.7 

3  X 21  Xi 

4.5 

1.31 

.9 

1.17 

.56 

.9 

.66 

.74 

.40 

.8 

3X2X1 

7.7 

2.25 

1.1 

1.92 

1.00 

.9 

.58 

.67 

.47 

.6 

3  X  2  X  I- 

4.1 

1.19 

1.0 

1.09 

.54 

1.0 

.49 

.39 

.26 

.6 

21 X  1?  X  t6b 

3.6 

1.07 

.8 

.53 

.37 

.7 

.42 

.19 

.18 

.4 

21 X  U  X  t3b 

2.3 

.67 

.8 

.34 

.23 

.7 

.37 

.12 

.11 

.4 

2  X  11  X  ts 

3.6 

1.07 

.6 

.40 

.30 

.6 

.52 

.28 

.23 

.5 

2  X  11 X  i5 

2.3 

.67 

.6 

.26 

.19 

.6 

.47 

.19 

.15 

.5 

If  X  11 X  t6b 

2.5 

.72 

.5 

.13 

.15 

.4 

.38 

.08 

.10 

.3 

*  pjstance  measured  from  outside  of  flange. 


PROPERTIES  OP  SECTIONS. 


87 


TAbiLE  XVI. 

Properties  of  Steel  T  Shapes— Equal  Legs. 


Size  of  T. 

Flange  by  Stem. 

Thickness. 

Weight  Per  Foot. 

Area  of  Section. 

Distance  of  Center  of  Gravity 
From  Flange.* 

Neutral  Axis 
Parallel  to 
Flange. 

Natural  Axis 
Square  to  Flange 
and  Coincident 
With  Stem. 

Moment  of  Inertia. 

Section  Modulus. 

Radius  of  Gyration. 
Inches. 

Moment  of  Inertia. 

Section  Modulus. 

Radius  of  Gyrat  ion. 

Inches. 

In. 

In. 

Lb. 

Sq. 

In. 

In. 

I. 

Q. 

R. 

I'. 

Q'. 

R'. 

4  X  4 

x 

13.60 

4.00 

1.18 

5.70 

2.02 

1.20 

2.80 

1.40 

.84 

4X4 

A 

10.40 

3.07 

1.15 

4.70 

1.64 

1.23 

2.19 

1.09 

.85 

3*  X  3* 

x 

11.70 

3.45 

1.06 

3.72 

1.52 

1.04 

1.89 

1.08 

.74 

X  3i 

7 

T7? 

10.40 

3.07 

1.03 

3.35 

1.35 

1.05 

1.65 

.94 

.73 

3?  X  3? 

5 

T?T 

6.80 

2.04 

.98 

2.30 

.93 

1.09 

1.07 

.61 

.73 

3  X  3 

1 

10.00 

2.94 

.93 

2.31 

1.10 

.88 

1.20 

.80 

.64 

3X3 

TJJ 

9.10 

2.67 

.92 

2.12 

1.01 

.90 

1.08 

.72 

.64 

3  X  3 

t 

7.80 

2.28 

.88 

1.81 

.86 

.90 

.90 

.60 

.63 

3X3 

y5s 

6.60 

1.95 

.86 

1.60 

.74 

.90 

.75 

.50 

.62 

2*  X  2* 

§ 

6.40 

1.89 

.76 

1.00 

.59 

.74 

.52 

.42 

.53 

2k  X  2k 

5 

Te> 

5.50 

1.62 

.74 

.87 

.50 

.74 

.44 

.35 

.52 

2k  X  2k 

5 

Tff 

4.90 

1.44 

.69 

.66 

.42 

.68 

.33 

.30 

.48 

2*  X  2k 

l 

4.10 

1.20 

.66 

.51 

.32 

.67 

.25 

.22 

.47 

2X2 

5 

TR 

4.30 

1.26 

.63 

.45 

.33 

.60 

.23 

.23 

.43 

2  X  2 

x 

3.70 

1.08 

.59 

.36 

.25 

.60 

.18 

.18 

.42 

If  X  If 

x 

3.10 

.90 

.54 

.23 

.19 

.51 

.12 

.14 

.37 

1?  X  If 

3 

T(T 

2.25 

.66 

.52 

.17 

.14 

.51 

.09 

.10 

.37 

4  X  H 

1 

2.55 

.75 

.42 

.15 

.14 

.49 

.08 

.10 

.34 

1 5-  X  H 

A 

1.85 

.54 

.44 

.11 

.11 

.45 

.06 

.07 

.31 

if  XH 

L 

2.04 

.60 

.40 

.08 

.10 

.36 

.05 

.07 

.27 

If  X  if 

T35 

1.55 

.45 

.38 

.06 

.07 

'  .37 

.03 

.05 

.26 

1  X  1 

1.23 

.36 

.32 

.03 

.05 

.29 

.02 

.04 

.21 

1  XI 

1 

e 

.90 

.26 

.29 

.02 

.03 

.29 

.01 

.02 

.21 

*  Distance  measured  from  outside  of  flange. 


88 


STRUCTURAL  DESIGN. 


TABLE  XVII. 

Properties  of  Steel  T  Shapes— Unequal  Legs. 


Size  of  T  Flange  by  Stem. 

Thickness. 

Weight  per  Foot. 

Area  of  Section. 

Distance  of  Center  of  Gravity 
From  Flange.  * 

Neutral  Axis 
Parallel  to 
Flange. 

Neutral  Axis 
Square  to  Flange 
and  Coincident 
With  Stem. 

Moment  of  Inertia. 

Section  Modulus. 

Radius  of  Gyration 
in  Inches. 

Moment  of  Inertia. 

Section  Modulus. 

Radius  of  Gyration 

in  Inches. 

In. 

In. 

Lb. 

Sq. 

In. 

In. 

I. 

Q. 

R. 

T. 

Q'. 

R'. 

6 

X  4 

t 

20.6 

6.06 

1.04 

7.66 

2.58 

1.13 

11.50 

3.83 

1.38 

6 

X  4 

17.0 

5.00 

.99 

6.37 

2.11 

1.13 

9.22 

3.07 

1.34 

5 

X  3 

JL 

13.5 

3.97 

.75 

2.60 

1.15 

.83 

5.23 

2.09 

1.18 

5 

X  2k 

3. 

10.4 

3.07 

.57 

1.24 

.64 

.64 

4.24 

1.70 

1.18 

4* 

X  3 

3. 

10.0 

3.00 

.75 

2.10 

.94 

.86 

3.10 

1.38 

1.04 

4i 

X  3 

A 

8.5 

2.55 

.73 

1.80 

.81 

.87 

2.60 

1.16 

1.03 

4 

X  3k 

i 

a 

12.5 

3.70 

1.01 

3.97 

1.60 

1.04 

2.88 

1.44 

.88 

4 

X3k 

1 

9.8 

2.88 

.92 

3.20 

1.24 

1.05 

2.18 

1.09 

.87 

4 

X  2k 

3. 

8 

8.6 

2.52 

.63 

1.20 

.62 

.69 

2.10 

1.05 

.92 

4 

X  2 

3. 

8 

7.9 

2.31 

.48 

.60 

.40 

.52 

2.12 

1.06 

.96 

3k 

X  4 

1 

a 

12.8 

3.75 

1.25 

5.50 

1.98 

1.21 

1.89 

1.08 

.72 

3k 

X  4 

t 

9.9 

2.91 

1.19 

4.30 

1.55 

1.22 

1.42 

.81 

.70 

3 

X  4 

l 

a 

11.9 

3.48 

1.32 

5.23 

1.94 

1.23 

1.21 

.81 

.59 

3 

X  3k 

l 

a 

10.9 

3.21 

1.12 

3.50 

1.49 

1.06 

1.20 

.80 

.62 

3 

X3k 

TS 

9.8 

2.88 

1.11 

3.30 

1.37 

1.08 

1.31 

.88 

.68 

3 

X  3k 

JL 

8 

8.5 

2.49 

1.09 

2.90 

1.21 

1.09 

.93 

.62 

.61 

p 

O 

X  2k 

f 

7.2 

2.10 

.71 

1.10 

.60 

.72 

.89 

.60 

.66 

3 

X2k 

6.1 

1.80 

.68 

.94 

.52 

.73 

.75 

.50 

.65 

3 

X  2 

3. 

8 

6.4 

1.88 

.55 

.53 

.37 

.56 

.85 

.57 

.71 

3 

XU 

.1 

8 

5.7 

1.68 

.40 

.22 

.20 

.34 

.85 

.57 

.75 

2k 

X  3 

3 

8 

7.2 

2.10 

.97 

1.80 

.87 

.92 

.54 

.43 

.51 

2k 

X  3 

TS 

6.1 

1.80 

.92 

1.60 

.76 

.94 

.44 

.35 

.51 

2k 

XH 

1 

4 

3.1 

.90 

.32 

.10 

.11 

.34 

.24 

.23 

.54 

*  Distance  measured  from  outside  of  flange. 


PROPERTIES  OF  SECTIONS. 


89 


TABLE  XVIII. 

Properties  of  Steel  Z  Bars. 


Neutral  Axis 

Neutral  Axis 

Perpendicular 

Coincident 

to  Web. 

With  Web. 

d 

d 

jd 

hH 

d 

•rH 

4-> 

0) 

fl 

hH 

t-H 

4 

0 

t>C 

Pi 

+j  ; 
0 

C  ' 

d 

0 

•rH 

H^> 

+3 

*H 

0) 

Cl 

HH 

Vh 

CO 

d 

d 

'd 

d 

0 

•rH 

CO 

d 

d 

ft 

d 

0 

•rH 

H-» 

c3 

£ 

fa 

m 

u 

<X> 

O 

0> 

0 

O 

>rH 

£ 

Vh 

O 

O 

krH 

H 

«+H 

m 

<D 

£ 

& 

CQ 

0 

o 

O 

1 

<+H 

o> 

rt 

<4_| 

d 

d 

<+H 

,d 

H-> 

ft 

<D 

ft 

ft 

4-S 

•  rH 

ft 

0 

2 

H 

fe  , 

•rH 

o» 

£ 

O 

0) 

a 

0 

a 

0 

•rH 

-*-> 

O 

0) 

m 

C 

d? 

oj 

P4 

a 

0 

s 

O 

O 

o» 

m 

O 

'd 

c3 

P5 

In. 

In. 

In. 

Lb. 

Sq.  In. 

j. 

Q. 

.K. 

p. 

Q'. 

12'. 

6 

3^ 

3. 

15.6  ' 

4.59 

25.32 

8.44 

2.35 

9.11 

2.75 

1.41 

6* 

3xs 

7 

ys 

18.3 

5.39 

29.80 

9.83 

2.35 

10.95 

3.27 

1.43 

6± 

3f 

X. 

21.0 

6.19 

34.36 

11.22 

2.36 

12.87 

3.81 

1.44 

6 

3i 

A 

22.7 

6.68 

34.64 

11.55 

2.28 

12.59 

3.91 

1.37 

6* 

6* 

3t95 

1 

25.4 

7.46 

38.86 

12.82 

2.28 

14.42 

4.43 

1.39 

3* 

Is 

28.0 

8.25 

43.18 

14.10 

2.29 

16.34 

4.98 

1.41 

6 

3* 

t 

29.3 

8.63 

42.12 

14.04 

2.21 

15.44 

4.94 

1.34 

6* 

6| 

3t95 

13 

TS 

7 

■jr 

32.0 

9.40 

46.13 

15.22 

2.22 

17.27 

5.47 

1.36 

3| 

34.6 

10.17 

50.22 

16.40 

2.22 

19.18 

6.02 

1.37 

5 

3|- 

xs 

t 

11.6 

3.40 

13.36 

5.34 

1.98 

6.18 

2.00 

1.35 

St’s 

3x6 

13.9 

4.10 

16.18 

6.39 

1.99 

7.65 

2.45 

1.37 

5p 

3f 

T5 

1 

<T 

16.4 

4.81 

19.07 

7.44 

1.99 

9.20 

2.92 

1.38 

5 

3i 

17.8 

5.25 

19.19 

7.68 

1.91 

9.05 

3.02 

1.31 

5* 

3x5 

A 

20.2 

5.94 

21.83 

8.62 

1.91 

10.51 

3.47 

1.33 

§| 

3| 

22.6 

6.64 

24.53 

9.57 

1.92 

12.06 

3.94 

1.35 

5 

3£ 

tt 

£ 

23.7 

6.96 

23.68 

9.47 

1.84 

11.37 

3.91 

1.28 

Sfs 

5* 

3x55 

3| 

26.0 

7.64 

26.16 

10.34 

1.85 

12.83 

4.37 

1.30 

it 

28.3 

8.33 

29.31 

11.44 

1.88 

14.36 

4.84 

1.31 

4 

St’s 

3} 

A 

8.2 

2.41 

6.28 

3.14 

1.62 

4.23 

1.44 

1.33 

4Jg 

T5 

1 

T5 

1 

10.3 

3.03 

7.94 

3.91 

1.62 

5.46 

1.84 

1.34 

4! 

4 

3t36 

3* 

31 

12.4 

13.8 

3.66 

4.05 

9.63 

9.66 

4.67 

4.83 

1.62 

1.55 

6.77 

6.73 

2.26 

2.37 

1.36 

1.29 

15.8 

4.66 

11.18 

5.50 

1.55 

7.96 

2.77 

1.31 

4I 

•*8 

Q  3 

'US 

9 

T5 

17.9 

5.27 

12.74 

6.18 

1.55 

9.26 

3.19 

1.33 

90 


STRUCTURAL  DESIGN. 


TABLE  XIX. 

Properties  op  Steel  I  Beams. 


Depth  of  Beam. 

Weight  per  Foot. 

Area. 

Thickness  of  Web. 

Width  of  Flange. 

Moment  of  Inertia. 
Neutral  Axis  Square 
to  Web  at  Center. 

Section  Modulus. 

Neutral  Axis  as  Before. 

Radius  of  Gyration. 

Neutral  Axis  as  Before. 

Inches. 

Moment  of  Inertia. 

Neutral  Axis  Coin¬ 

cident  With  Center 
Line  of  Web. 

Radius  of  Gyration. 

Neutral  Axis  as  Before. 

Inches. 

In. 

Lb. 

Sq. 

In. 

In. 

In. 

I. 

Q. 

R. 

T. 

R'. 

20 

90 

26.4 

.78 

6.75 

1506.10 

150.60 

7.55 

42.30 

1.27 

20 

80 

23.5 

.69 

6.38 

1345.10 

134.50 

7.55 

33.20 

1.19 

20 

75 

22.1 

.66 

6.16 

1246.90 

124.70 

7.53 

28.20 

1.13 

20 

65 

19.1 

.50 

6.00 

1148.60 

114.90 

7.76 

25.50 

1.16 

15 

75 

22.1 

.81 

6.29 

720.40 

96.00 

5.72 

34.60 

1.25 

15 

66f 

19.7 

.65 

6.13 

676.30 

90.10 

5.87 

31.70 

1.27 

15 

60 

17.6 

.52 

6.00 

637.70 

85.00 

6.02 

29.20 

1.29 

15 

50 

14.7 

.45 

5.75 

529.70 

70.60 

6.00 

21.00 

1.20 

15 

42 

12.4 

.40 

5.50 

429.60 

57.30 

5.90 

14.00 

1.08 

12 

55 

16.1 

.63 

6.00 

358.10 

59.70 

4.72 

25.20 

1.25 

12 

40 

11.8 

.39 

5.50 

281.30 

46.90 

4.90 

16.80 

1.20 

12 

31 J 

9.3 

.35 

5.13 

220.50 

36.70 

4.88 

10.30 

1.04 

10 

40 

11.8 

.58 

5.21 

178.50 

35.70 

3.89 

13.50 

1.07 

10 

33 

9.7 

.37 

5.00 

161.30 

32.30 

4.08 

11.80 

1.10 

10 

30 

8.8 

.45 

4.89 

134.50 

26.90 

3.90 

8.10 

0.96 

10 

25 

7.3 

.31 

4.75 

122.50 

24.50 

4.00 

7.30 

0.99 

9 

27 

7.9 

.31 

4.75 

110.60 

24.60 

3.72 

9.10 

1.07 

9 

23j 

6.9 

.35 

4.58 

89.00 

19.80 

3.60 

5.90 

0.93 

9 

21 

6.2 

.27 

4.50 

84.30 

18.70 

3.70 

5.56 

0.95 

8 

27 

7.9 

.48 

4.56 

77.60 

19.40 

3.14 

6.91 

0.93 

8 

22 

6.4 

.29 

4.38 

69.70 

17.40 

3.30 

6.02 

0.97 

8 

18 

5.2 

.25 

4.13 

56.80 

14.20 

3.30 

3.95 

0.87 

7 

20 

5.7 

.28 

4.09 

47.60 

13.60 

2.89 

4.86 

0.92 

7 

15 

4.4 

.23 

3.88 

37.10 

10.60 

2.89 

3.12 

0.84 

6 

15 

4.3 

.25 

3.52 

26.40 

8.81 

2.47 

2.74 

0.79 

6 

12 

3.6 

.22 

3.38 

21.70 

7.25 

2.47 

1.91 

0.73 

5 

13 

3.8 

.26 

3.13 

15.70 

6.28 

2.06 

1.98 

0.72 

5 

9| 

2.9 

.21 

3.00 

12.10 

4.87 

2.06 

1.29 

0.67 

4 

10 

2.9 

.39 

2.69 

6.84 

3.42 

1.53 

0.89 

0.55 

4 

n 

2.2 

.20 

2.50 

5.86 

2.93 

1.63 

0.70 

0.56 

4 

6 

1.8 

.18 

2.19 

4.59 

2.30 

1.61 

0.38 

-  -  -  w  ” 

0.47 

PROPERTIES  OF  SECTIONS. 


91 


TABLE  XX. 

Radii  of  Gyration  for  Two  Angles  Placed  Back  to  Back. 

Equal  Legs. 

Radii  of  gyration  given  correspond  to  directions  of  the 

arrowheads. 


Size. 

Inches. 

Thick¬ 

ness. 

Inches. 

Radii  of  Gyration. 

7*0- 

n- 

r2. 

rs- 

8  X  8 

1 

9 

2.50 

3.32 

3.45 

3.58 

6  X6 

7 

T 

1.87 

2.64 

2.83 

2.92 

6  X  6 

TS 

1.87 

2.50 

2.67 

2.76 

6  X  6 

t 

1.88 

2.49 

2.66 

2.75 

5  X5 

7 

T 

1.49 

2.17 

2.35 

2.45 

5  X  5 

t 

1.55 

2.20 

2.38 

2.48 

5  X5 

5 

8 

1.56 

2.09 

2.27 

2.36 

4  X  4 

H 

1.24 

1.83 

2.03 

2.12 

4  X  4 

1.23 

1.68 

1.86 

1.95 

4  X  4 

A 

1.24 

1.67 

1.85 

1.94 

3iX3i 

1 

1.04 

1.51 

1.70 

1.81 

3iX3i 

1 

1.07 

1.47 

1.66 

1.75 

3iX3i 

TS 

1.08 

1.46 

1.65 

1.74 

3  X  3 

1 

.94 

1.40 

1.59 

1.69 

3  X  3 

x 

.93 

1.25 

1.43 

1.53 

2t  X  2| 

X 

.85 

1.15 

1.34 

1.44 

2f  X2} 

1 

9 

.82 

1.19 

1.39 

1.49 

2hX2i 

1 

¥ 

.76 

1.12 

1.31 

1.42 

2s  X  2? 

x 

.77 

1.05 

1.25 

1.34 

2iX2i 

x 

.70 

1.05 

1.25 

1.35 

2?  X  2| 

x 

.69 

.96 

1.14 

1.24 

2iX2i 

t3<j 

.69 

.94 

1.12 

1.22 

2  X  2 

x 

.62 

.95 

1.15 

1.26 

2  X  2 

A 

.62 

.84 

1.03 

1.13 

it  XU 

i 

e 

.47 

.63 

.77 

.92 

92 


STRUCTURAL  DESIGN. 


TABLE  XXI. 

Radii  of  Gyration  for  Two  Angles  Placed  Back  to  Back 
Long  Leg  Vertical. 

Unequal  Legs. 

Radii  of  gyration  given  correspond  to  directions  of  the 

arrowheads. 


Size. 

Inches. 

Thick¬ 

ness. 

Inches. 

Radii  of  Gyration. 

To- 

n. 

t2. 

r3. 

6  X  4 

X 

1.95 

1.68 

1.87 

1.97 

6  X  4 

1 

1.93 

1.50 

1.67 

1.76 

5  X3| 

4 

1.59 

1.44 

1.63 

1.73 

5  XBi 

4 

1.60 

1.34 

1.51 

1.61 

5  X  3 

4 

1.62 

1.23 

1.42 

1.52 

5  X  3 

T55 

1.61 

1.09 

1.26 

1.36 

4*  X  3 

4 

1.43 

1.25 

1.44 

1.55 

44  X  3 

TB3 

1.45 

1.13 

1.31 

1.40 

4  X34 

4 

1.24 

1.53 

1.72 

1.83 

4  X  34 

t5s 

1.26 

1.41 

1.58 

1.69 

4  X  3 

4 

1.23 

1.20 

1.39 

1.50 

4  X  3 

TS 

1.27 

1.17 

1.35 

1.45 

34  X  3 

t 

1.06 

1.27 

1.46 

1.56 

3*  X  3 

t6$ 

1.10 

1.21 

1.39 

1.49 

34  X  24 

t9s 

1.10 

1.04 

1.23 

1.34 

34-  X  24 

1.12 

.96 

1.17 

1.24 

3  X  24 

.93 

1.07 

1.27 

1.37 

3  X  24 

X 

.95 

1.00 

1.18 

1.28 

3  X  2 

l 

t 

.92 

.80 

1.00 

1.10 

3  X  2 

i_ 

.96 

.75 

.93 

1.04 

24  X  14 

.70 

.60 

.79 

.91 

24  X  H 

t3s 

.72 

.57 

.75 

.86 

PROPERTIES  OF  SECTIONS. 


93 


TABLE  XXII. 

Radii  of  Gyration  for  Two  Angles  Placed  Back  to  Back, 
Short  Leg  Vertical. 

Unequal  Legs. 

Radii  of  gyration  given  correspond  to  directions  of  the 

arrowheads. 


Size. 

Inches. 

Thick¬ 

ness. 

Inches. 

Radii  of  Gyration. 

T-o- 

n. 

r2- 

r3. 

7  X3i 

7 

TB 

.95 

3.37 

3.56 

3.66 

6  X4 

7 

J 

1.19 

2.94 

3.13 

3.23 

6  X  4 

i 

1.17 

2.74 

2.92 

3.02 

5  X3± 

i 

1.01 

2.39 

2.58 

2.68 

5  X3£ 

i 

1.02 

2.27 

2.45 

2.55 

5  X  3 

i  / 

.86 

2.50 

2.69 

2.79 

5  X  3 

.85 

2.33 

2.51 

2.61 

44  X  3 

4 

.86 

2.18 

2.38 

2.46 

4iX3 

A 

.87 

2.06 

2.25 

2.33 

4  X3i 

4 

1.05 

1.85 

2.04 

2.14 

4  X  3y 

A 

1.07 

1.73 

1.91 

2.00 

4  X  3 

t 

.83 

1.84 

2.03 

2.13 

4X3 

A 

.89 

1.79 

1.97 

2.07 

34  X  3 

4 

.87 

1.57 

1.76 

1.87 

34X3 

T3 

.90 

1.53 

1.71 

1.81 

34X24 

9 

T5 

.72 

1.66 

1.85 

1.95 

34X24 

JL 

.74 

1.58 

1.76 

1.86 

3  X24 

A 

.73 

1.40 

1.59 

1.69 

3  X2| 

.75 

1.32 

1.49 

1.60 

3  X  2 

4 

.55 

1.42 

1.62 

1.72 

3X2 

JL 

.57 

1.39 

1.57 

1.68 

24X2 

JL 

.56 

1.16 

1.35 

1.46 

24X2 

A 

.60 

1.10 

1.28 

1.39 

G 


94 


STRUCTURAL  DESIGN. 


COLUMNS. 

The  columns  used  in  building  construction  are  usually  of 
3tone,  wood,  cast  iron,  or  structural  steel.  Stone  columns 
are  more  frequently  met  with  as  features  of  architectural 
treatment  than  as  supporting  members  of  the  structure. 
When  they  are  used  as  structural  members,  they  are  generally 
so  proportioned  that  they  fail  by  crushing,  and  their  strength 
depends  on  the  compressive  resistance  of  the  material. 

Wooden  columns  have  their  principal  use  in  such  build¬ 
ings  as  large  stores,  factories,  and  warehouses,  constituting 
part  of  a  system  of  slow-burning  construction  which  many 
consider  to  be  superior  to  partially  fireproof  construction 
embodying  cast-iron  columns.  The  argument  advanced  is 
that,  in  case  of  fire,  the  wooden  columns  will  become  charred 
upon  the  outside,  and,  thus  protected,  the  body  of  the  column 
will  retain  its  strength  and  successfully  support  the  loads 
above  ;  while  under  similar  conditions  cast-iron  columns  will 
become  intensely  heated,  and,  if  water  is  played  upon  them, 
will  snap  and  thus  prematurely  destroy  the  building.  Cast- 
iron  columns  are  rapidly  being  superseded  by  those  built  up 
of  rolled-steel  sections,  or,  as  they  are  called,  structural-steel 
columns.  This  is  evidently  due  to  the  low  price  of  structural 
steel,  and  also  to  the  unreliability  of  cast  iron  under  the 
action  of  fire  and  suddenly-applied  loads.  Another  objection 
to  cast-iron  columns  is  the  difficulty  of  making  rigid  connec¬ 
tion  between  the  columns  of  the  several  floors,  and  also  of 
the  floorbeams  to  the  columns.  This  objection  becomes 
serious  when  the  height  of  the  building  increases  to  8  or  12 
stories ;  it  is  on  record  that,  on  account  of  this  lack  of  rigidity 
in  the  connections,  a  certain  building  in  New  York  was 
forced  by  the  wind  11  inches  out  of  pflumb. 

Strength  of  Columns. — The  strength  of  columns  depends 
upon  their  length  and  shape  of  cross-section.  Long  columns 
will  fail  by  bending  under  less  load  than  will  short  columns. 
Of  two  columns  having  the  same  sectional  area,  the  one 
having  the  material  in  the  section  distributed  farthest  from 
the  central  axis  of  the  column  will  be  stronger  than 
one  having  the  bulk  of  material  located  near  the  center. 


COLUMNS. 


95 


If  all  the  material  composing  the  cross-section  of  a  column 
could  be  located  at  a  distance  from  the  center  equal  to  the 
radius  of  gyration,  the  column  would  possess  equal  strength 
to  resist  flexure  as  though  the  material  was  distributed  over 
the  cross-section.  Hence,  in  formulas  for  calculating  the 
strength  of  columns,  both  the  radius  of  gyration  and  the 
length  are  to  he  taken  into  consideration. 


WOODEN  COLUMNS. 

The  formula  for  determining  the  strength  of  wooden 
columns  having  flat  or  square  ends  was  deduced  from 
exhaustive  tests  of  full-size  specimens,  made  at  the  Water- 
town  Arsenal,  Mass.,  and  may  be  expressed  as  follows : 


in  which  S  —  ultimate  strength  of  column  per  square 
inch  of  section ; 

U  —  ultimate  compressive  strength  of  the 
material  per  square  inch  ; 
l  —  length  of  the  column  in  inches ; 
d  =  dimension  of  the  least  side  of  the  column 
in  inches. 

The  above  formula  may  he  applied  to  all  wooden  columns, 
the  length  or  height  of  which  is  not  under  10  times  nor  over 

i 

45  times  the  dimension  of  the  least  side.  In  other  words,  ^ 

should  not  be  less  than  10  nor  more  than  45.  If  the  length 
is  less  than  10  times  the  least  side,  the  direct  compressive 
strength  of  the  material  per  square  inch,  multiplied  by  the 
sectional  area  of  the  column  in  square  inches,  will  give 
the  strength  of  the  column.  If  the  length  is  over  45  times  the 
least  side,  this  formula  will  not  apply  ;  in  such  cases,  provision 
must  he  made  for  bracing  the  column  in  all  directions,  or  the 
load  upon  it  must  be  greatly  reduced.  Columns  of  this 
dimension,  however,  seldom  occur  in  building  practice. 

Having  determined  S,  the  breaking  load  per  square  inch 
of  section,  the  safe  load  per  square  inch  will  be  obtained  by 
dividing  by  the  required  factor  of  safety,  4,  5,  or  fl,  This 


96 


STRUCTURAL  DESIGN. 


result,  multiplied  by  the  sectional  area,  will  give  the  safe  load 
the  column  will  sustain. 

Example.— What  safe  load  will  a  10"  X  12"  Northern 
yellow-pine  column  20  ft.  long  support,  provided  a  factor  of 
safety  of  5  is  used  ? 

Solution.— In  the  formula  S  =  U—(-^J-,\,  the  value 

\  100  d) 

of  U  for  Northern  yellow  pine  is  given  in  Table  IX,  page  71, 
as  4,000;  l  is  equal  to  20  ft.  X  12  in.  =  240  in.;  and  the  least 
side  of  the  column,  or  d,  is  10  in.  By  substituting  these 

values  in  the  formula,  S  =  4,000  —  (  =  3>040 

the  ultimate  or  breaking  strength  of  the  column  per  square 
inch  of  cross-section. 

Then,  3,040  -f-  5  (factor  of  safety)  =  608  lb.,  the  safe  strength 
of  the  column  to  compression  per  square  inch  of  section. 

The  sectional  area  of  the  column  is  12  in.  X  10  in.  =  120 
sq.  in.;  hence,  the  safe  load  that  the  column  will  support 
is  equal  to  608  X  120,  or  72,960  lb. 

Details  of  Design.— For  slow-burning  construction,  the  Fire 
Underwriters’  Association  will  not  allow  the  use  of  square 
wooden  columns  less  than  8  in.  on  a  side ;  so,  although  the 
actual  required  size  of  column  to  safely  sustain  the  load 
might  be  much  less  than  8  in.,  it  is  not  advisable  in  first-class 
buildings  of  this  construction  to  use  wooden  columns  less 
than  this  size. 

Large  timber  posts — that  is,  posts  not  under  8  or  10  in. 
least  dimension— are  considered  as  offering  more  resistance  to 
fire  than  cast-iron  columns;  hence,  they  are  often  used, 
especially  in  mill  construction,  in  preference  to  the  latter. 

Care  should  be  taken  in  selecting  timber  for  columns  or 
posts  to  obtain  only  seasoned  wood,  without  wind  or  twist, 
free  from  defects  likely  to  affect  its  strength.  The  ends  of  the 
posts  should  be  cut  square,  so  as  to  take  a  uniform  bearing  at 
the  base  and  cap  plates.  The  timber  commonly  used  for  posts 
is  yellow  pine,  which  includes  the  Northern,  Southern,  or 
Georgia  pines;  white  pine,  spruce,  and  Oregon  spruce  are 
frequently  used,  and  in  some  instances,  oak. 

Details  of  the  usual  cast-iron  caps  and  bases  which  are 
used  with  wooden  columns  are  given  on  page  197. 


TABLE  XXIII. 

API'KOXIMATE  LREaKING  LOADS  FOR  NORTHERN  YELLOW-PlNE  COLUMNS,  IN  THOUSANDS  OF  Lb. 
Calculated  by  the  formula :  S  =  U—  U  =  4,0001b. 


COLUMNS. 


97 


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98 


STRUCTURAL  DESIGN. 


CAST-IRON  COLUMNS. 


A  formula  for  obtaining  the  strength  of  cast-iron  columns 
having  flat  or  square  ends  is, 

S  =  - 


u 


1  + 


— V 

V  3,600  R-J 


in  which 


,600  R- 

S  =  breaking  strength  of  column  in  lb. 

per  sq.  in.  of  section  ; 
l  =  length  of  column  in  inches ; 

*R 2  =  square  of  the  least  radius  of  gyra¬ 
tion  ; 

f  U  —  ultimate  compressive  strength  of 
cast  iron  in  lb.  per  sq.  in. 

Having  calculated  the  value  of  S,  the  safe  strength  per 
square  inch  may  be  obtained  by  dividing  by  the  factor  of 
safety.  The  safe  load  on  the  column  is  then  found  by  multi¬ 
plying  this  value  by  the  sectional  area  of  the  column  in 
square  inches. 

Example. — Find  the  proper  working  load  for  a  10-in.  square 
cast-iron  column,  20  ft.  long,  using  a  factor  of  safety  of  6,  the 
thickness  of  the  metal  being  1  in. 

Solution.— The  ultimate  compressive  strength  U  of  cast 
iron  in  lb.  per  sq.  in.,  according  to  Table  VIII,  page  70,  is  81,000 ; 
the  length  l  equals  20  ft.  X  12  in.  =  240  in. ;  and  the  formula 
for  determining  A2  for  a  hollow  square  column  is,  according 
to  Table  XII,  page  83, 

b2  +  b'2 


R2  = 

Substituting  figures, 

jgj  =  102  +  82 


12  * 
100  +  64 


=  13.6. 


12  12 

Upon  substituting  these  values  in  the  formula,  there  results, 
81,000  _  81,000 
2.17 


S 


/  240  X  240  \ 
\3,600  X  13.6/ 


37,327  lb.  per  sq.  in. 


,600  X  13. 

Using  a  factor  of  safety  of  6,  the  safe  load  per  sq.  in.  of  sec¬ 
tion  is  37,327  -T-  6  ==  6,221  lb.  Since  the  net  area  section  is 


*  For  values  of  R2,  see  page  83.  f  See  page  70. 


COLUMNS. 


99 


100  sq.  in.  —  64  sq.  in.  =  36  sq.  in.,  the  entire  load  that  the 
column  will  safely  sustain  is  equal  to  6,221  lb.  X  36  sq.  in.  = 
223,956  lb. 

Design  of  Cast-Iron  Columns.— Since  cast-iron  columns  are 
usually  more  or  less  in  a  state  of  internal  strain,  due  to  the 
unequal  cooling  of  the  metal  in  the  molds,  and  also  because 
of  the  uncertain  nature  of  the  casting,  a  factor  of  safety  of 
from  6  to  8  should  be  used  in  designing  them. 

Fig.  10  shows  a  design  for  a  circular  cast-iron  column.  A 
shows  the  elevation  for  the  cap  and  brackets  supporting  steel 
floorbeams.  Special  care  ...  , 

,  ,  ,  ,  ,  .  i  Wood  Column 

should  be  exercised  m 
the  design  of  the  bracket 
a,  the  web  being  made, 
as  shown  at  A,  to  extend 
to  the  edge  of  the  plate  m, 
and  with  the  general  out¬ 
line  of  its  front  edge 
forming  an  angle  of  about 
60°  with  m.  If  the  web 
is  made  as  shown  by  full 
line  at  a  in  B,  and  the 
beam  takes  a  bearing 

upon  the  edge  of  the  plate  m,  the  tendency  will  be  to  fracture 
the  edge  of  the  bracket.  It  is  well  to  have  at  least  fillets  in 
all  the  corners  of  the  casting,  and  also  to  thicken  the  metal 
in  the  column  adjacent  to  the  brackets,  as  shown  at  b. 

The  bolt  holes  /  should  be  always  drilled,  either  in  the 
casting  or  in  the  steel  beams  after  the  latter  are  in  place, 
because,  if  the  holes  are  cored  in  the  casting  and  the  holes 
punched  in  the  beams  at  the  mill,  it  is  likely  that  the  beams 
will  be  supported  entirely  by  the  shear  of  the  bolts,  without 
bearing  upon  the  bracket  at  all.  The  bolts  should  tit  the  bolt 
holes  /  closely,  and  it  is  best,  if  practicable,  to  drill  the  holes 
in  both  beams  and  cast-iron  flange  ;  this  will  insure  as  rigid  a 
connection  as  is  possible  with  this  form  of  construction. 

The  strengthening  webs  of  the  base  should  be  placed  in 
the  most  effective  position,  that  is,  on  the  diagonals,  as  shown 
in  Fig.  10;  ifiplaced  on  t}ie  diameters,  the  corners  will  hav? 


Plan  of  Baje 


Fig.  10. 


100 


STRUCTURAL  DESIGN. 


a  tendency  to  break  off,  thus  reducing  the  bearing  surface  of 
the  base. 

In  designing  cast-iron  columns  a  good  rule  to  observe  is  to 
have  the  thickness  of  the  metal  in  the  body  of  the  column 
not  under  f  in.  If  made  less  than  this,  the  difficulty  of  obtain¬ 
ing  sound  castings  is  increased,  because  the  metal,  in  flowing 
into  the  mold,  is  liable  to  cool  before  completely  filling  it,  and 
thus  weak  spots  and  dangerous  flaws  are  formed. 

Inspection  of  Cast-Iron  Columns.— All  building  castings,  and 
especially  columns,  should  be  carefully  inspected  before 
being  placed  in  the  building.  Air  bubbles  and  blowholes  are 
a  common  and  dangerous  source  of  weakness,  and  should  be 
searched  for  by  tapping  the  casting  with  a  hammer.  Bubbles 
or  flaws  filled  in  with  sand  from  the  mold,  or  purposely 
stopped  with  loam,  cause  a  dullness  in  the  sound.  The  cast¬ 
ing  should  be  free  from  flaws  of  any  kind,  with  the  exterior 
surface  smooth  and  clean,  and  the  edges  sharp  and  perfect. 
An  uneven  or  wavy  surface  indicates  unequal  shrinkage. 
Cast-iron  columns  should  be  straight,  and  cored  directly 
through  the  center,  the  metal  being  as  nearly  as  possible  of 
uniform  thickness  throughout.  It  is  not  unusual  to  find  cast- 
iron  columns,  designed  to  be  £  in.  thick  throughout,  1£  in. 
on  one  side  and  i  in.  on  the  other. 

The  base  and  cap  of  a  cast-iron  column  should  be  turned 
accurately,  being  true  and  perpendicular  to  the  center  line. 

Fireproofing  of  Cast-Iron  Columns. — Cast-iron  columns  sub¬ 
jected  to  the  intense  heat  of  a  conflagration  are  liable  to 
destruction  when  water  is  played  upon  them.  In  consequence, 
especially  when  located  in  important  situations  and  when 
their  failure  in  case  of  fire  would  practically  destroy  the  build¬ 
ing,  they  should  be  thoroughly  fireproofed.  There  are  several 
means  employed  to  accomplish  this.  The  columns  may  be 
incased  in  a  light  cast-iron  shell,  an  air  space  of  from  1  to  3  in. 
being  left  between  the  column  and  the  casing ;  this  space  is 
sometimes,  but  not  usually,  filled  with  a  incombustible,  non- 
conductive  material.  Two  rough  and  one  finish  coats  of  good 
hard  mortar  plaster  laid  upon  an  expanded  metal  casing,  sur¬ 
rounding  the  column,  with  an  air  space  between,  make  a 
good  fireproof  protection.  Terra-cotta  tile  is  also  much  used- 


COLUMNS. 


101 


TABLE  XXIV. 


Breaking  Loads  for  Square  Cast-Iron  Columns. 
In  thousand  pounds.  U  —  81,000. 


Dimen. 
of  Side. 
In. 

Thick¬ 

ness. 

In. 

Length  of  Column  in  Feet. 

8  ft. 

10  ft. 

12  ft. 

14  ft. 

16  ft. 

18  ft. 

20  ft. 

6 

1 

594 

6 

1 

700 

584 

6 

f 

820 

685 

567 

6 

929 

770 

638 

535 

7 

1 

2 

775 

664 

573 

494 

430 

7 

f 

840 

725 

625 

532 

460 

395 

7 

i 

1,090 

935 

810 

688 

589 

505 

440 

7 

7 

8 

1,220 

1,060 

915 

770 

660 

570 

491 

7 

1 

1,368 

1,180 

1,020 

860 

780 

625 

540 

8 

f 

1,162 

1,040 

915 

805 

708 

621 

540 

8 

f 

1,380 

1,218 

1,060 

930 

815 

710 

582 

8 

7 

8 

1,550 

1,370 

1,220 

1,065 

930 

814 

700 

8 

1 

1,730 

1,530 

1,340 

1,169 

1,018 

882 

770 

8 

n 

1,900 

1,660 

1,450 

1,248 

1,098 

950 

835 

9 

i 

1,391 

1,262 

1,138 

1,013 

908 

800 

715 

9 

* 

1,643 

1,473 

1,338 

1,192 

1,060 

940 

831 

9 

7 

8 

1,861 

1,678 

1,510 

1,340 

1,180 

1,060 

938 

9 

1 

2,100 

1,880 

1,690 

1,500 

1,320 

1,176 

1,040 

•  9 

n 

2,300 

2,070 

1,840 

1,630 

1,450 

1,276 

1,135 

10 

i 

1,934 

1,784 

1,584 

1,467 

1,328 

1,190 

1,064 

10 

n_ 

2,184 

2,000 

1,820 

1,643 

1,485 

1,334 

1,200 

10 

l 

2,440 

2,250 

2,040 

1,850 

1,660 

1,490 

1,345 

10 

H 

2,890 

2,650 

2,400 

2,140 

1,930 

1,730 

1,550 

10 

li 

3,040 

2,710 

2,470 

2,225 

1,992 

1,780 

1,600 

11 

7 

2,510 

2,340 

2,150 

1,950 

1,783 

1,623 

1,484 

11 

l 

2,810 

2,650 

2,430 

2,200 

2,020 

1,821 

1,680 

11 

li 

3,100 

2,920 

2,670 

2,440 

2,230 

2,030 

1,840 

11 

li 

3,430 

3,180 

2,930 

2,660 

2,440 

2,200 

1,990 

12 

l 

3,150 

2,970 

2,770 

2,570 

2,370 

2,180 

1,980 

12 

H 

3,520 

3,300 

3,007 

2,850 

2,620 

2,420 

2,230 

12 

li 

3,870 

3,620 

3,370 

3,120 

2,870 

2,640 

2,430 

12 

H 

4,170 

3,900 

3,600 

3,350 

3,080 

2,820 

2,570 

13 

H 

3,890 

3,690 

3,460 

3,250 

3,140 

2,780 

2,560 

13 

H 

4,290 

4,070 

3,820 

3,580 

3.340 

3,060 

2,830 

13 

H 

4,650 

4,400 

4.130 

3.940 

3,570 

3,000 

3,040 

13 

H 

5,000 

4,740 

4.420 

4,130 

3.830 

3,520 

3,240 

14 

li 

4,740 

4,530 

4,280 

4.000 

3,760 

3,510 

3,260 

14 

If 

5,060 

4,870 

4,620 

4,340 

4,050 

3,770 

3,520 

14 

5,520 

5,270 

4,980 

4,680 

4,870 

4,060 

3,800 

14 

if 

5,900 

5,610 

5,300 

5,980 

4,650 

4,330 

4,030 

6 

6 

6 

6 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

11 

11 

11 

11 

12 

12 

12 

12 

13 

13 

13 

13 

14 

1 1 

1  l 

14 


STRUCTURAL  DESIGN. 


TABLE  XXV. 

iking  Loads  for  Round  Cast-Iron  Columns. 
In  thousand  pounds.  U  —  81,000. 


Thick- 

Length  of  Column  in  Feet. 

ness. 

In. 

8  ft. 

10  ft. 

12  ft. 

14  ft. 

16  ft. 

18  ft. 

20  ft. 

1 

a 

418 

5 

8 

505 

412 

i 

570 

465 

374 

7 

8 

651 

525 

423 

347 

1 

a 

560 

474 

393 

332 

270 

IL 

8 

655 

566 

476 

402 

332 

287 

f 

820 

658 

544 

456 

384 

324 

280 

7 

8 

880 

732 

610 

510 

425 

360 

313 

1 

971 

810 

670 

559 

470 

396 

339 

t 

850. 

735 

631 

542 

462 

400 

352 

1 

1,000 

910 

743 

640 

545 

468 

405 

7 

8 

1,120 

960 

810 

710 

620 

529 

455 

1 

1,260 

1,082 

930 

785 

675 

578 

502 

1,360 

1,185 

1,005 

865 

732 

625 

545 

1 

1,040 

923 

810 

710 

620 

535 

480 

1 

1,220 

1,073 

950 

820 

720 

628 

560 

7 

8 

1,360 

1,200 

1,050 

918 

805 

595 

614 

1 

1,550 

1,362 

1,192 

1,039 

900 

758 

682 

If 

1,710 

1,500 

1,300 

1,130 

958 

851 

751 

f 

1,420 

1,280 

1,141 

1,020 

900 

798 

705 

i- 

1,640 

1,495 

1,318 

1,170 

1,036 

910 

820 

i 

1,830 

1,580 

1,460 

1,292 

1,143 

1,010 

895 

if 

2,030 

1,810 

1,470 

1,310 

1,160 

1,110 

980 

! 

1,640 

1,510 

1,363 

1,260 

1,120 

1,000 

895 

7 

8 

1,840 

1,680 

1,540 

1,385 

1,250 

1,113 

990 

1 

2,100 

1,923 

1,740 

1,570 

1,420 

1,258 

1,119 

If 

2,300 

2,110 

1,920 

1,720 

1,550 

1,370 

1,217 

* 

1,869 

1,740 

1,600 

1,440 

1,310 

1,200 

1,080 

7 

8 

2,130 

1,960 

1,800 

1,630 

1,490 

1,360 

1,223 

1 

2,380 

2,180 

2,020 

1,840 

1,670 

1,500 

1,360 

If 

2,580 

2,350 

2,180 

1,990 

1,800 

1,620 

1,470 

f 

2,020 

1,900 

1,740 

1,620 

1,480 

1,363 

1,265 

7 

8 

2,400 

2,250 

2,100 

1,920 

1.760 

1,590 

1,465 

1 

2,660 

2,480 

2,320 

2,120 

1,940 

1,745 

1,610 

If 

2,920 

2,720 

2,540 

2,310 

2,120 

1,900 

1,750 

T 

2,600 

2,450 

2,310 

2,160 

1,970 

1,820 

1,670 

1 

2,930 

2,700 

2,580 

2,390 

2,140 

2,090 

1,880 

if 

3,250 

3,090 

2,850 

2,670 

2,440 

2,300 

2.070 

H 

3,560 

3,360 

3,140 

2,910 

2,660 

2,440 

2,250 

COLUMNS. 


103 


STRUCTURAL-STEEL  COLUMNS. 


The  method  of  securing  the  ends  of  a  column  greatly 
influences  its  strength.  While  wooden  and  cast-iron  columns 
usually  occur  in  building  construction  with  flat  or  square 
ends,  structural-steel  columns  are  often  used,  having  either 
hinged,  flat  or  square,  and  flxed  ends.  Where  the  ends  are 
securely  fixed,  so  that  the  column  is  likely  to  fail  in  the  shaft, 
before  the  end  connections  are  ruptured,  greater  strength  is 
developed  than  with  columns  having  hinged  or  pinned  ends. 
Columns  having  flat  or  square  ends  are  somewhat  stronger 
than  hinged-end  columns,  hut  not  so  strong  as  those  having 
their  ends  firmly  secured. 

The  strength  of  structural-steel  columns  may  he  determined 
hy  the  following  formulas : 


S  = 


For  Fixed  Ends. 
U 


1  + 


/  J2  V 

V  36,000  Rn-J 


S 


For  Square  Ends. 
U 


1  + 


Y 

V  24,000  Ii-  ) 


For  Pin  Ends. 


1  +  (  18,000  R*  ) 

in  which  &  =  ultimate  strength  of  column  in  pounds  per 
square  inch  ; 

U  —  ultimate  compressive  strength  of  the 
material  in  pounds  per  square  inch  ; 
l  —  length  of  column  in  inches ; 

*R  =  least  radius  of  gyration. 


The  value  of  U  for  structural  steel  is  usually  taken  at  from 
52,000  to  54,000  lb.  for  soft  steel,  and  as  high  as  60,000  for 
medium  steel. 

Having  determined  S,  the  safe  load  per  square  inch  is 
found  by  dividing  S  by  the  factor  of  safety.  This  quotient, 
multiplied  by  the  area  of  the  section,  will  give  the  safe  load 
the  column  will  sustain. 


*  See  page  81. 


I 


104 


STRUCTURAL  DESIGN. 


Example. — What  safe  load  will  a  square-end  structural- 
■y  steel  column,  20  ft.  long,  having  the  sec¬ 

tion  shown  in  Fig.  11,  support,  taking 
the  ultimate  compressive  strength  at 
52,000  lb.  per  sq.  in.,  and  using  a  factor 
of  safety  of  5  ? 

Solution.— First  calculate  the  radius 
of  gyration  about  both  the  axes  XX  and 
Y  Y,  by  the  method  given  on  page  81. 
This  will  determine  the  least  radius  of 
gyration,  which  in  this  case  is  around 
Fig.  11.  the  axes  Y  Y,  and  is  approximately  2.13 

in.  The  value  of  R 2  will  then  be  2.13  X  2.13  =  4.53.  The  value 
of  l,  the  length  of  the  column  in  inches,  is  20  (ft.)  X  12  (in.) 
=  240  in.;  andf2  =  240X240  =  57,600.  Substituting  the  above 
values  in  the  formula, 

U  „  '52,000 


rp 

"V-- 

ej 

r 

-r!r — A" 

-  e* 

U 

F 

■ 

' 

S  = 


s  = 


1  +  (24,000#“)  1+( 


57,600 


=  34,000, 


,000i?2/  '  V  24,000  x  4.53/ 

Which  is  the  ultimate  strength  of  the  column  in  pounds  per 
square  inch  of  section. 

The  total  sectional  area  is  as  follows : 

*  Area  of  4  —  5"  X  3"X  rs"  angles  =  2.40  X  4  =  9.60  sq.  in. 

f  Area  of  TBS"  X  10"  web-plate  =  10  X  .3125  =  3.125  sq.  in. 


Total  area  of  section  =  12.725  sq.  in. 


Then  34,000  (ultimate  strength  of  the  column  in  pounds 
per  square  inch  of  section)  X  12.72  (sq.  in.)  =  432,480  lb.  The 
factor  of  safety  required  being  5,  the  safe  load  that  the 
column  will  support  is  432,480  -4-  5  =  86,496  lb. 

The  formulas  above  given  being  somewhat  awkward  to 
use,  more  convenient  ones  have  been  deduced,  and  while 
they  give  somewhat  different  values  for  S  than  those  obtained 
by  the  previously  stated  formulas,  the  differences  are  on  the 
side  of  safety.  These  formulas  may  be  applied  to  columns 
whose  lengths  are  between  50  and  150  least  radii  of  gyration  ; 


*  See  table,  page  86. 

f  For  table  of  decimal  equivalents,  see  page  53. 


COL  UMNS. 


105 


that  is,  if  the  radius  of  gyration  of  a  column  is  2  in.,  these 
formulas  will  apply  to  columns  whose  lengths  are  between 
100  and  300  in. 


Fixed  ends, 
Square  ends, 
Pin  ends, 


Medium  Steel. 

S  =  60,000  —  210  4 

JX 

S  =  60,000  -  230  4 

JX 

S  =  60,000  —  260  4 


Soft  Steel. 

S  =  54,000  —  185  4 

JX 

S  =  54,000  —  200  4 

JX 

S  =  54,000  -  225  4 


In  these  formulas, 

S  =  ultimate  or  breaking  strength  of  the  column  in 
pounds  per  square  inch  of  sectional  area ; 
l  =  length  of  the  column  in  inches ; 

R  —  least  radius  of  gyration  in  inches. 

Example. — What  is  the  ultimate  strength  in  pounds,  per 
square  inch  of  section,  for  a  fixed-end  column  22  ft.  long,  the 
least  radius  of  gyration  for  the  section  being  2.5  in.  and  the 
material  being  medium  steel  ? 


Solution.— The  formula  S' 


60,000  —  210=,  by  substitu- 

JX 


ting  the  values  for  l  and  R,  becomes 


S  =  60,000  -  210  =-=  =  37,824  lb., 
z.o 

the  ultimate  strength  per  square  inch  of  column  section. 

Structural  columns  are  usually  considered  as  having  square 
ends,  and  a  factor  of  safety  of  4  is  generally  allowed.  The  fol¬ 
lowing  formulas  will  give  the  allowable  stress  in  pounds  per 
square  inch  which  such  columns  will  sustain  : 

Medium  Steel.  Soft  Steel. 

S  =  15,000  —  574  S  =  13,500  —  5o4 

JX  JX 


The  formula  for  medium-steel  columns  is  for  lengths  over 
50  times  the  least  radius  of  gyration ;  that  for  soft-steel  col¬ 
umns  is  for  lengths  over  30  times  the  least  radius  of  gyration. 
For  columns  of  dimensions  less  than  these  figures,  a  safe  load 
of  12,000  lb.  per  sq.  in.  of  section  can  safely  be  assumed. 

No  column  should  be  used  whose  length  is  greater  than  150 
least  radii  of  gyration,  or  whose  length  exceeds  45  times  the 
least  dimension  of  the  column. 


106 


STRUCTURAL  DESIGN. 


Design  of  Structural-Steel  Columns.— Structural-steel  col¬ 
umns  should  be  so  designed  that,  where  several  lengths  are 
connected  end  to  end,  the  splice  may  be  made  in  a  rigid  and 
secure  manner ;  they  should  also  be  so  constructed  as  to 
facilitate  connecting  floorbeams  or  girders  on  all  sides.  All 
beam  connections  to  the  column  should  be  carefully  designed 
and  provided  with  sufficient  rivets,  to  avoid  failure  of  the 
connections  by  shearing  of  the  rivets.  Rivets  in  columns 
should  be  so  spaced  as  not  to  exceed  3  in.  center  to  center,  at 
the  ends  of  the  column,  for  a  distance  equal  to  twice  the 
width  of  the  column.  The  distance  between  rivets  from 
center  to  center,  in  a  direction  parallel  with  the  line  of  strain, 
should  not  exceed  16  times  the  least  tliickness  of  metal  of  the 
parts  joined  ;  and  the  distance  from  center  to  center  between 
the  rivets  at  right  angles  to  the  line  of  strain  should  not 
exceed  32  times  the  least  thickness  of  metal.  Further  con¬ 
siderations  in  regard  to  rivets  and  rivet  spacing  are  given  on 
pages  128  to  133. 


BEAMS  AND  GIRDERS. 

A  body  resting  upon  supports  and  liable  to  transverse  stress 
is  called  a  beam.  Beams  are  designated  by  the  number  and 
location  of  the  supports,  and  may  be  either  simple,  cantilever, 
fixed,  or  continuous.  A  simple  beam  js  one  that  is  supported  at 
each  end,  the  distance  between  its  supports  being  the  span. 
A  cantilever  is  a  beam  that  has  one  or  both  ends  overhanging 
the  support ;  a  beam  having  one  end  firmly  fixed  and  the 
other  end  free  is  a  cantilever.  A  fixed  beam  is  one  that  has 
both  ends  firmly  secured.  A  continuous  beam  is  one  which 
rests  upon  more  than  two  supports. 


MOM  ENTS. 

The  moment  of  a  force  around  a  fixed  point  is  equal  to  the 
force  multiplied  by  its  lever  arm,  which  is  the  perpendicular 
distance  from  the  line  of  action  of  the  force  to  the  point ;  this 
product  is  called  foot-pounds  or  inch-pounds,  according  to  the 
unit  used.  Thus  in  (a),  Fig.  12,  the  moment  about  c  =  10  lb. 


BEAMS  AND  GIRDERS. 


107 


' 10  ft.  =  100  ft. -lb.  In  {b)  the  moment  about  c  is  10  lb.  X  8  ft. 
=  80  ft.-lb.  Likewise  in  (c)  the  moment  around  c  is  20  lb. 
<  24  in.  =  480  in. -lb.  In  (d),  the  beam  is  supported  at  c  ;  the 
Dree  a  has  a  moment  about  c  of  30 
b.  X  8  ft.  =  240  ft.-lb.,  acting  in  a 
irection  contrary  to  the  motion  of 
lock  hands.  The  force  b  has  a  mo- 
aent  about  c  of  20  lb.  X  10  ft.  =  200 
t.-lb.,  acting  in  the  direction  of  motion 
if  clock  hands.  It  is  evident  that  the 
>eam  will  turn  around  c  in  the  direction 
>f  the  greater  moment,  with  a  moment 
if  240 ft.-lb.  — 200 ft.-lb.  =  40 ft.-lb.;  the 
ieam  is,  therefore,  not  in  equilibrium. 

;fa  force  of  4  lb.  be  added  to  b,  creating 
i  moment  of  4  lb.  X  10  ft.  =  40  ft.-lb., 
n  counterbalance  the  moment  of  40 
't.-lb.  tending  to  rotate  the  beam,  the 
atter  will  then  be  in  equilibrium. 

Eence,  moments  tending  to  produce 
rotation  in  the  same  direction  are  alike, 
ind  should  be  added ;  those  acting  in  opposite  directions 
ire  unlike,  and  the  smaller  should  be  deducted  from  the 
greater.  The  total  moment  of  a  system  of  forces  about  a  point 
is  the  algebraic  sum  of  the  moments  of  all  the  forces  around 
that  point.  If  a  body  is  in  equilibrium ,  the  algebraic  sum  of 
the  moments  of  the  forces  acting  upon  that  body  is  zero  about 
any  point  in  that  body. 


30  t\ 

ISO  Uk 
-lOftir] 

c‘ 

> 

(d) 
Fig.  12. 


I 


TV 

SL 


TV 

a 


TV 


THEORY  OF  BEAMS. 

If  a  beam  is  loaded  as  at  W  W  W,  Fig.  13,  the  weights  pro¬ 
duce  reactions  at  the  supports.  These 
forces,  or  reactions,  Ri,  and  _R2,  oppose 
the  action  of  the  weights  and  their 
combined  action  must  equal  the  total 
weight.  The  weights  and  reactions, 
constituting  the  external  forces,  tend  to  produce  bending  in 
the  beam,  and  are  resisted  by  the  internal  forces,  consisting 
of  the  strength  of  the  fibers  composing  the  beam.  In  a  simple 


Fig.  13. 


I 


108 


STRUCTURAL  DESIGN. 


beam,  the  effect  of  loading  is  to  shorten  the  upper  fibers,  and 
to  lengthen  the  lower  ones.  Somewhere  between  the  top  and 
bottom  of  the  cross-section  are  located  fibers  which  are 
neither  shortened  nor  lengthened  ;  this  position  is  called  the 
neutral  axis  (see  page  75).  In  steel  and  like  material  of 
homogeneous  nature,  the  neutral  axis  passes  through  the 
center  of  gravity  of  the  section. 

At  any  point  in  the  length  of  a  beam,  the  tendency  to 
produce  bending  is  equal  to  the  algebraic  sum  of  the  moments 
of  the  external  forces  at  that  point ;  this  moment  is  called  the 
bending  moment.  A  beam  resists  bending  at  any  point  by  the 
resistance  of  its  particles  to  extension  or  compression,  the 
sum  of  the  moments  of  which  about  the  neutral  axis  of  the 
cross-section  is  called  the  moment  of  resistance ,  or  resisting 
moment.  For  a  beam  to  be  sufficiently  strong  to  sustain  the 
load,  the  moment  of  resistance  must  equal  the  bending  moment. 
If  the  moment  of  resistance  is  expressed  in  inch-pounds,  the 
bending  moment  must  likewise  be  reduced  to  inch-pounds. 

Reactions. — The  reactions  or  supporting  forces  of  any  beam 
or  structure  must  equal  the  loads  upon  it.  If  the  load  upon  a 
simple  beam  is  uniformly  distributed,  applied  at  the  center  of 
the  span,  or  symmetrically  placed  and  of  equal  amount  upon 
each  side  of  the  center,  the  reactions  Rx  and  R2  will  each  be 
equal  to  one-half  the  load.  When  the  loads  are  not  symmet¬ 
rically  placed,  the  reactions  are  found  by  the  principle  of 
moments  in  the  following  manner : 

Fig.  14  represents  a  simple  beam  supporting  loads  Wx,  W2, 

and  W3 ;  Ms  the  span  or  distance 
between  the  reactions  Rx  and  R2 ;  a, 
b,  and  c  are  the  distances  from  the 
reaction  Rx  to  the  loads  Wx,  W2,  JF3, 
respectively.  Then,  the  right-hand 
reaction,  R*  = 

( W\  X  a)  +  ( TF2  X  b)  +  ( W3  X  c) 
l 

This  formula  expressed  in  a  general  rule  is :  To  find  the 
reaction  at  either  support,  multiply  each  load  by  its  distance  from 
the  other  support,  and  divide  the  sum  of  these  products  by  the 
distance  between  supports. 


- fr- 


off  d'h”; 


it, 


Fig.  14. 


1 

No 


BEAMS  AND  GIRDERS. 


109 


Since  the  sum  of  the  reactions  must  equal  the  sum  of  the 
toads,  if  one  reaction 
is  found,  the  other  can 
be  obtained  by  sub¬ 
tracting  the  known  one 
from  the  sum  of  the 
loads. 

Example  .—What 
are  the  reactions  at  R± 
and  R2,  Fig.  15  ? 

Solution. — The  lever  arm  of  a  uniformly  distributed  load 
is  always  the  distance  from  the  center  of  moments  to  the 
center  of  gravity  of  the  load.  The  total  uniform  load  a  is 
3,000  X  10  =  30,000  lb.,  and  the  distance  of  its  center  of  gravity 
from  Ri  is  13  ft.  The  moments  of  the  loads  about  Ri  are  as 
follows:  J 

4,000  lb.  X  4  ft.  =  16,000  ft.-lb. 

30,000  lb.  X  13  ft.  =  390,000  ft.-lb. 

9,000  lb.  X  20  ft.  =  180,000  ft.-lb. 

Total  =  586,000  ft.-lb. 

The  distance  from  Rx  to  R<>  is  30  ft.;  hence,  586,000  -r-  30 
=  19,533}  lb.,  the  reaction  at  i?2.  As  the  sum  of  the  loads  is 
43,000  lb.,  the  reaction  at  R\  is  43,000—  19,533}  =  23,466}  lb. 

Shear.— The  loads  and  reactions,  besides  causing  bending 
or  flexure,  create  shearing  stresses  in  the  beam  by  their 
opposing  tendency;  that  is,  as  the  reactions  act  upwards  and 
the  loads  downwards,  the  effect  is  to  shear  the  fibers  of  the 
beam  vertically.  At  any  section  of  a  beam,  the  shear  is  equal  to 
either  reaction  minus  the  sum  of  the  loads  between  that  reaction 
and  the  section  considered.  The  maximum  shear  is  always 
equal  to  the  greatest  reaction.  For  a  simple  beam  with  a 
uniformly  distributed  load,  the  maximum  shear  is  at  the  sup¬ 
ports,  and  is  equal  to  one-half  the  load,  or  to  the  reaction ; 
the  shear  changes  at  every  point  of  the  loaded  length,  the 
minimum  shear  being  zero  at  the  center  of  the  span.  The 
maximum  shear  in  a  simple  beam  having  a  single  load  con¬ 
centrated  at  the  center  is  equal  to  one-half  the  load,  and  is 
uniform  throughout  the  beam.  Where  a  beam  supports 


© 


20  ft. 


§13  ft. - -i 

dftl 


© 
© 
a 


V—IO  ftr-A 

- 30  ft~ 

Fig.  15. 


110 


STRUCTURAL  DESIGN. 


several  concentrated  loads,  changes  in  the  amount  of  shear 
occur  only  at  the  points  where  the  loads  are  applied. 

For  example,  in  the  beam  loaded  as  shown  in  Fig.  16,  the 
shear  on  the  line  a  b  is  equal  to  the  reaction  Rx  of  40  lb.  minus 
the  load  n  of  10  lb.,  or  30  lb.  The  shear  between  o  and  p,  on 

the  line  c  d,  is  equal  to 
the  reaction  R\  of  40  lb. 
minus  the  sum  of  the 
loads  n,  m,  and  o,  or  zero. 
Working  from  the  same 
reaction  JSi,  the  shear  on 
the  beam  between  p  and 
q  is  equal  to  Ri  —  (n  +  m 
+  o  +  p),  or  40  lb.  —  55  lb. 
=  —15  lb.  Thus,  all  the 
beam  to  the  left  of  o  is  in  what  may  be  called  positive  shear, 
while  to  the  right  of  p  the  shear  is  in  the  opposite  direction, 
and  may  be  called  negative  shear.  It  is  evident  that  there  is 
a  section  in  the  beam— for  instance,  cd— -where  the  shear 
changes  from  positive  (+)  to  negative  (—);  that  is,  it  passes 
through  zero,  or  changes  sign. 

Example. — (a)  What  is  the  maximum  shear  on  the  beam 
shown  in  Fig.  15?  (5)  What  is  the  shear  11  ft.  from  the  right 
support?  (c)  Where  does  the  shear  change  sign ? 

Solution. — (a)  Taking  the  center  of  moments  at  R»,  the 
reaction  at  Ri  is  as  follows : 

9,000  lb.  X  10  ft.  =  90,000  ft.-lb. 

3,000  lb.  X  10  ft.  X  17  ft.  =  510,000  ft.-lb. 

4,000  lb.  X  26  ft.  =  104,000  ft.-lb. 

Total  =  704,000  ft.-lb. 

Then,  704,000  ~  30  —  23,466|  lb.,  the  reaction  Ri.  The  total 
load  being  43,000  lb.,  the  reaction  R.2  is  43,000  —  23,466|  = 
19,5331  lb.;  hence  the  maximum  shear  is  R\.  (6)  The  reac¬ 
tion  Ro  being  19,533j  lb.,  and  there  being  but  a  load  of  9,000  lb. 
between  it  and  a  section  11  ft.  distant,  the  shear  at  the  latter 
point  is  19,533?  —  9,000  =  10,533?  lb.  (c)  Working  from  Ru 
the  first  load  is  4,000  lb.,  and  the  shear  at  this  point  is  23,466f  — 


3  3  3  3  3  3 

$  3  §  3  3  5 


« 

n 

m 

o 

! 

P 

Q 

1 

*  *  * 


Fig.  16. 


BEAMS  AND  GIRDERS. 


Ill 


4,000  =  19,466f  lb.  Then  enough  of  the  uniform  load  must 
he  taken  to  equal  this  amount.  It  is  clear  that  the  shear 
becomes  negative  somewhere  in  the  uniform  load,  since  the 
latter  is  30,000  lb.,  or  more  than  19,466f  lb.  Dividing  19,466f  by 
3,000,  the  load  per  foot,  the  result  is  6.48  ft.,  the  distance  from 
left  end  of  uniform  load  to  point  where  the  shear  changes 
sign ;  hence  the  distance  from  R^  is  4  +  4  +  6.48  =  14.48  ft. 

Bending  Moment. — The  algebraic  sum  of  the  moments  of  the 
external  forces  about  any  point  in  a  beam  is  the  bending 
moment  at  that  point ;  that  is,  the  bending  moment  at  any 
point  is  the  moment  about  that  point  of 
either  reaction  minus  the  sum  of  the. 
moments  of  the  intermediate  loads 
about  the  same  point.  For  example, 
the  bending  moments  at  several  points 
on  the  beam  shown  in  Fig.  17  are  as 
follows :  At  Wi  =  Ri  a ;  at  W2  =  Rx  (a +b)  —  Wx  b ;  at  W3 
=  R\  (u  — (—  — j—  c )  —  [  TIT;  c  -f-  TFi  ( b  c)],  or  R%  d ,  etc. 


GFiCFcF 


-E, 


Fig.  17. 


JR, 


The  bending  moment  varies,  depending  on  the  shear,  and 
attains  a  maximum  value  at  the  point  where  the  shear  changes 
sign.  If  the  loads  are  concentrated  at  several  points,  the 
maximum  bending  moment  will  be  under  the  load  at  which 
the  sum  of'  all  the  loads  between  one  support  up  to  and 
including  the  load  in  question  first  becomes  equal  to,  or 
greater  than,  the  reaction  at  the  support.  Hence,  to  find  the 
maximum  bending  moment  in  any  simple  beam : 

Rule. — Compute  the  re - 
actions  and  determine  the 
point  where  the  shear 
changes  sign.  Calculate 
the  moment  about  this  point 
of  either  reaction,  and  of 
each  load  between  the  re¬ 
action  and  the  point,  and 
subtract  the  sum  of  the  latter 
a  moments  from  the  former. 

Example. — What  is  the  maximum,  bending  moment  in 
inch-pounds  of  the  beam  loaded  as  shown  in  Fig.  18? 

Solution. — Taking  moments  about  7?i  and  remembering 


112 


STRUCTURAL  DESIGN. 


that  a  uniform  load  has  the  same  moment  as  an  equal  load 
concentrated  at  the  center  of  gravity  of  the  uniform  load, 
the  total  moment  is  found  to  be  358,250  ft.-lb.  The  span  being 
25  ft.,  the  reaction  R2  is  358,250  -f-  25  =  14,330  lb.  As  the 
sum  of  the  loads  is  32,500  lb.,  the  reaction  Rx  is  32,500  —  14,330 
=  18,170  lb.  This  is  the  greatest  reaction  and  greatest  shear. 

Beginning  at  Rx  and  adding  the  loads  in  succession,  it  is 
found  that  the  load  of  10,000  lb.  plus  the  uniform  load  between 
the  reaction  and  the  load  d  is  10,000  +  (500  X  13)  =  16,500  lb., 
which  is  less  than  the  left  reaction,  or  Rx ;  when,  however, 
the  load  d  is  added,  the  sum  of  the  loads  is  greater  than  the 
reaction ;  hence,  the  shear  changes  sign  under  the  load  d, 
and  the  greatest  bending  moment  is  also  at  that  point.  Tak¬ 
ing  moments  about  the  point  under  the  load  d,  the  moment 
of  Rx  is  18,170  x  13  =  236,210  ft.-lb.  The  moments  of  the  loads 
between  d  and  Rx  are  : 

6,500  lb.  X  6i  ft.  =  42,250  ft.-lb. 

10,000  lb.  X  7  ft,  =  70,000  ft.-lb. 

Total  =  112,250  ft.-lb. 


Then,  236,210  ft.-lb.  —  112,250  ft.-lb.  =  123,960  ft.-lb.,  the 
maximum  bending  moment.  The  bending  moment  in  inch- 
pounds  is  123,960  ft.-lb.  X  12  =  1,487,520  in.-lb. 

If  W  =  the  load  and  L  —  the  span,  the  maximum  bend¬ 
ing  moment  in  a  simple  beam  uniformly  loaded  is  —  X 

£  & 


WL 
8  ' 


( 


^  is  the  distance  from  the  center  of 
4 


beam  to  center  of  gravity  of  each  half  of  the  uniform  load.) 

The  maximum  bending  moment  in  a  beam  with  a  load  con- 

W  L 

centrated  at  the  center  is  — — .  Thus,  a  beam  uniformly  loaded 

will  carry  safely  twice  as  much  as  if  the  load  were  concentrated  at 
the  center. 

While,  by  the  preceding  principles,  the  bending  moment 
in  any  beam  supported  at  one  or  two  supports  may  be  deter^ 
mined,  it  is  more  convenient  to  use  concise  formulas.  The 
following  table  gives  formulas  for  the  maximum  bending 
moment,  maximum  safe  loads,  and  greatest  deflections  (or 
sag),  for  beams  loaded  and  supported  in  different  ways ; 


BEAMS  AND  GIRDERS. 


113 


TABLE  XXVI. 


114 


STRUCTURAL  DESIGN . 


Resisting  Moment.— The  moment  of  resistance  of  a  beam  is 
the  sum  of  the  moments  about  the  neutral  axis  of  all  the 
stresses  in  the  fibers  composing  the  section.  The  safe  resisting 
moment  of  any  beam  section  is  equal  to  the  product  of  the  safe 
fiber  stress  and  the  moment  of  inertia  divided  by  the  distance  from 
the  neutral  axis  to  the  extreme  fibers.  If  I  is  the  moment  of 
inertia,  c  the  distance  in  inches  from  the  neutral  axis  to  the 

extreme  fibers,  and  S  the  safe  fiber  stress  in  pounds  per  square 

IS  I 

inch,  the  resisting  moment  M\  =  - — ;  but  since  -  =  Q,  the 

c  c 

section  modulus  (see  page  82),  Mi  —  QS;  that  is,  the  safe 
resisting  moment  is  equal  to  the  safe  fiber  stress  multiplied  by  the 
section  modulus.  To  obtain  the  safe  unit  fiber  stress,  the 
modulus  of  rupture  of  the  material  (see  Tables  VIII,  IX,  X) 
is  divided  by  the  required  factor  of  safety. 

Example. — What  is  the  safe  resisting  moment  of  a  Northern 
yellow-pine  beam  10  in.  wide  X  12  in.  deep,  using  a  factor  of 
safety  of  4  ? 

Solution.— In  the  formula  M i  =  QS,  the  section  modulus 

b  d 2 

Q  for  a  rectangular  section  (by  Table  XII)  is  — r- ,  or,  for  the 

O 

10  V  19  V  19 

given  section,  Q  =  —  - - - =  240.  From  Table  IX,  the 

D 

modulus  of  rupture  for  Northern  yellow  pine  is  6,000  lb.;  the 
desired  factor  of  safety  being  4,  the  safe  unit  fiber  stress  S  is 
6,000  -4-  4  =  1,500  lb.  Then  QS  =  1,500  X  240  =  360,000,  the 
safe  resisting  moment,  or  Mi ,  of  the  beam  section  in  inch- 
pounds. 

A  beam  will  ’safely  support  a  given  load  when  the  safe 
resisting  moment  M\,  in  inch-pounds,  is  equal  to,  or  greater 
than,  the  bending  moment  M  also  in  inch-pounds.  Econom¬ 
ical  design  requires  that  the  safe  resisting  moment  be  but 
little,  if  any,  in  excess  of  the  bending  moment,  having  regard, 
also,  to  the  nearest  commercial,  or  stock,  sizes. 

Deflection. — Stiffness  in  beams  is  as  important  as  strength. 
Lack  of  stiffness  causes  vibrations,  springy  floors,  deflection, 
or  sagging,  producing  plaster  cracks  in  ceilings.  To  prevent 
excessive  deflection,  shallow  beams  must  be  avoided.  The 
deflection  of  beams  carrying  plastered  ceilings  should  not 
exceed  3-|(j  of  the  span.  Usually  this  limit  is  not  exceeded 


BEAMS  AND  GIRDERS. 


115 


when  the  depth  of  wooden  beams  is  at  least  ^  the  span.  In 
dwellings,  the  full  floor  load  being  seldom  realized,  and  as 
bridging  is  used  between  joists,  their  depth  may,  with  safety, 
be  14  in.  for  a  span  as  great  as  22  ft.  The  depth  of  rolled-steel 
beams  should  not  be  less  than  &  the  span,  and  that  of  plate 
girders  not  less  than  XV  If  doubt  exists  as  to  the  stiffness  of 
a  beam,  its  deflection  should  be  calculated  by  formulas  from 
Table  XXYI,  and  if  found  excessive,  the  load  should  be 
diminished,  or  the  size  of  beam  increased. 

Example.— A  6"  X  10"  white-oak  beam,  uniformly  loaded 
with  5,000  lb.,  has  a  span  of  16  ft.  8  in.  What  is  the  deflection ? 

5  Wl 3 

Solution. — From  Table  XXVI,  the  deflection  =  ^ET 


from  Table  IX,  E  —  1,100,000 ;  I  -  -yy  = 

Hence  deflection  =  5  X  5,000  X  8,000,000  = 
nence,  aenecuon  3g4  x  1  100  000  x  500 


b  ds  6  X  1,000 


12 
.94  in. 


=  500. 


CALCULATION  OF  BEAMS. 

Wooden  Beams.— These  are  principally  used  to  support  a 
uniformly  distributed  load,  consequently  a  convenient  for¬ 
mula  for  determining  directly  the  safe  strength  of  rectangular 
beams  uniformly  loaded  is  useful,  and  may  be  deduced  from 
the  foregoing  principles  as  follows :  The  bending^ moment  M 

in  foot-pounds  is  or  in  inch-pounds,  — 5  .  Placing 


8  ’  - "  '  8 

this  equal  to  the  resisting  moment,  M\,  or  Q  S,  there  results 


12WL 


8  QS 


8 


=  QS, or  12WL  =  8  QS;  whence  W=  -yyy 


3 

5  d2 


QS 

L 


For  a  rectangular  beam,  the  section  modulus  Q  —  g  >  an(^ 


r  2  S  b  d?  Sbd\ 

the  above  formula  may  be  written  II  =  y  jr  — y  —  9  ^  ’  0 
and  d  are  in  inches  and  L  in  feet.  This  formula  expressed  in 


words  is  as  follows : 

Rule. — The  safe  uniformly  distributed  load  in  pounds  for  a 
rectangular  beam  is  equal  to  the  safe  unit  fiber  stress  multiplied  by 
the  breadth  in  inches  and  by  the  square  of  the  depth  in  in<  /jes,  and, 
the  prodiict  divided  by  nine  time?  the  span  in  feet, 


116 


STRUCTURAL  DESIGN. 


TABLE  XXVII. 

Safe  Uniformly  Distributed  Loads  for  Rectangular 
Wooden  Beams,  1  Inch  Thick. 


Depth  of  Beam. 


in 

Feet.. 

6" 

7" 

8" 

9" 

10" 

12" 

14" 

16" 

5 

800 

1,090 

1,420 

1,800 

2,220 

3,200 

4,380 

5,690 

6 

665 

910 

1,190 

1,500 

1,850 

2,670 

3,650 

4,740 

7 

570 

780 

1,020 

1,290 

1,590 

2,290 

3,130 

4,060 

8 

500 

680 

890 

1,130 

1,390 

2,000 

2,740 

3,560 

9 

445 

610 

790 

1,000 

1,230 

1,780 

2,430 

3,160 

10 

400 

540 

710 

900 

1,110 

1,600 

2,190 

2,840 

11 

365 

495 

650 

820 

1,010 

1,450 

1,990 

2,590 

'  12 

335 

450 

590 

750 

930 

1,330 

1,820 

2,370 

13 

310 

420 

550 

690 

860 

1,230 

1,690 

2,200 

14 

285 

390 

510 

640 

800 

1,150 

1,570 

2,040 

15 

265 

360 

480 

600 

740 

1,070 

1,460 

1,900 

16 

250 

340 

450 

560 

700 

1,000 

1,370 

1,780 

17 

235 

320 

420 

530 

650 

940 

1,290 

1,680 

18 

220 

300 

400 

500 

620 

890 

1,220 

1,590 

19 

210 

290 

380 

480 

590 

840 

1,150 

1,500 

20 

200 

272 

360 

450 

560 

800 

1,090 

1,420 

21 

lbo 

260 

340 

430 

530 

760 

1,040 

1,360 

22 

180 

248 

325 

410 

510 

730 

1,000 

1,300 

23 

175 

237 

310 

390 

480 

700 

950 

1,240 

24 

165 

228 

297 

380 

460 

670 

910 

1,190 

25 

160 

218 

285 

360 

450 

640 

880 

1,140 

26 

155 

210 

275 

350 

430 

620 

840 

1,100 

27 

149 

202 

265 

330 

410 

590 

810 

1,060 

28 

143 

195 

255 

315 

400 

570 

780 

1,020 

29 

138 

188 

246 

307 

380 

550 

750 

980 

30 

134 

182 

237 

297 

370 

530 

730 

950 

Safe  load  for  any  thickness  =  safe  load  for  1  in.  X  thick¬ 
ness  in  inches. 

Thickness  for  any  load  =  lopd  a-  safe  load  for  l  in. 


BEAMS  AND  GIRDERS. 


117 


The  Tames  given  are  safe  loads  for  spruce  or  white-pine 
beams,  with  a  factor  of  safety  of  4.  For  oak,  or  Northern 
yellow  pine,  multiply  tabular  values  by  1£,  and  for  Georgia 
yellow  pine,  multiply  tabular  values  by  1|. 

Table  XXVII  is  calculated  fora  maximum  fiber  stress  of  1,000 
lb.  per  sq.  in.,  but  may  be  used  with  any  fiber  stress  by  dividing 
that  stress  by  1,000  and  multiplying  by  the  tabular  value;  thus, 
for  a  stress  of  800  lb.,  the  safe  load  is  .8  the  tabular  value. 

Loads  given  below  the  heavy  zigzag  line  produce  deflec¬ 
tions  likely  to  crack  plastered  ceilings. 

Example. — What  uniformly  distributed  load  will  a  hem¬ 
lock  joist  3  in.  wide  X  14  in.  deep  safely  support,  the  span 
being  20  ft.,  and  the  factor  of  safety,  5? 

Solution.— In  the  formula  W  =  =  3,500  lb.,  the 


modulus  of  rupture  of  hemlock  (see  Table  IX),  5,  the  factor 
of  safety,  =  700  lb.  per  sq.  in.;  b  =  3  in.;  d 2  =  14  in.  X  14  in. 
=  196 ;  and  L  =  20  ft.  Then  the  safe  uniformly  distributed 
700  X  3  X  196 


load  IF  = 


9X20 


2,287  lb. 


Otherwise,  from  Table  XXVII,  the  safe  load  with  a  fiber 
stress  of  1,000  lb.  per  sq.  in.  for  this  beam  =  the  load  for  1  in. 
width  X  the  width,  or  1,090  X  3  =  3,270  lb. ;  but  for  a  safe 


700 

stress  of  700  lb.  per  sq.  in.,  the  safe  load  is  =  .7  of  3,270  lb. 
=  2,289  lb. 


The  following  example  shows  how  to  calculate  the  size  of 
a  rectangular  beam  necessary  to  support  a  given  load  : 

Example.— What  .size  Georgia  yel- 
low-pine  joist  would  be  required  to 
support  two  concentrated  loads  placed 
as  shown  in  Fig.  19,  using  a  factor  of 
safety  of  4  ? 


3  JT-, 

1 


20  ft- 


Solution.— The  reaction  R»  = 


Ri  Fig. 19.  Ro 
(3,000  X  3)  +  (2,000  X  15) 


20 


=  1,950  lb.,  and  J2i  =  (3,000  +  2,000) —1,950  =  3,050  1b.  The 
greatest  bending  moment  31  is  found,  by  trial,  to  be  under  the 
2,000  lb.  load,  and  is  equal  to  1,950  lb.  X  5  ft.  =  9,750  ft.-lb., 
or  117,000  in. -lb.  Such  a  section  must  be  obtained  that  will 
]agve  a  resisting  moment  equal  to  this  bending  moment  of 


118 


STRUCTURAL  DESIGN. 


117,000  in.-lb.  The  modulus  of  rupture  of  y ellow  pine,  7,000  lb., 
divided  by  the  factor  of  safety  4,  gives  a  unit  fiber  stress  of 
1,750  lb.  Then  as  the  resisting  moment  of  any  beam  section, 

Mi  —  QS,  by  transposition,  Q  =  —,  or  - 1  ^--Q-  =  67,  the 
required  section  modulus. 

bd2 

By  Table  XII,  for  any  rectangular  section,  Q  =  — — .  By 

O 

trial,  the  value  of  Q  for  a  3"  X 10"  beam  is  50 ;  as  this  is 
evidently  too  small,  try  a  3"  X  12"  beam ;  for  this  Q  is  72, 
which  is  ample,  and  this  beam  is  selected,  being  the  nearest 
stock  size. 

Rolled-Steel  Beams.— In  calculating  the  size  of  steel  beam 
sections,  the  greatest  bending  moment  is  first  calculated ; 
then  the  section  modulus  required  is  equal  to  the  bending 
moment  in  inch-pounds  divided  by  the  safe  unit  fiber  stress, 
obtained  by  dividing  the  modulus  of  rupture  of  the  material 
by  the  factor  of  safety.  This  may  be  expressed  in  formula  as 

Q  =  2_>  in  which,  as  before,  Q  —  section  modulus,  If  = 

bending  moment  in  inch-pounds,  and  S  =  safe  or  allowable 
unit  fiber  stress  in  pounds  per  square  inch.  Having  found 
the  section  modulus,  the  proper  size  channel  or  I  beam  may 
be  selected  from  Tables  XIII  and  XIX,  the  one  being  chosen 
which  has  a  section  modulus  (see  column  headed  Q)  nearest 
to  that  required,  the  deepest  beam  having  the  required  section 
modulus  and  lightest  weight  being  preferred. 

In  selecting  rolled  structural-steel  beams  the  depth  of  the 
beam  in  inches  should  never  be  less  than  one-half  the  span  in  feet, 
in  order  to  avoid  excessive  deflection,  which  causes  cracks  in 
plastered  ceilings.  For  instance,  if  the  span  is  20  ft.,  a  beam 
should  be  not  less  than  10  in.  deep. 

Example.— The  brick-and-concrete  floor  of  an  office  build¬ 
ing  weighs  110  lb.  per  sq.  ft.,  and  is  designed  for  a  live  load 
of  40  lb.  per  sq.  ft.  The  span  of  the  beams  is  20  ft.,  and  they 
are  spaced  5  ft.  on  centers.  Using  a  factor  of  safety  of  4,  what 
size  steel  I  beams  are  required  ? 

Solution.— Total  load  is  110  lb.  +  40  lb.  =  150  lb.  per  sq.  ft; 
floor  surface  supported  upon  one  beam  is  20  ft.  X  5  ft.  =  100 
sq.  ft. ;  total  load  on  one  beam  is  100  sq.  ft.  x  150  lb.  =  15,000  lb., 


BEAMS  AND  GIRDERS. 


119 


=  IF.  The  load  being  uniformly  distributed,  the  bending 

,  nr  v  mil  wttt  •  WL  15,000  X  20  „„  ,nA 

moment,  3/,  by  Table  XX VI,  is— 3—  =  — ! — ^ —  =  37,500 

O  O 


ft. -lb.  or  450,000  in. -lb.  The  modulus  of  rupture  for  struc¬ 
tural  steel  being  about  60,000  lb.  (see  Table  VIII),  and  the 
required  factor  of  safety,  4,  the  allowable  unit  fiber  stress 


is  60,000  -f-  4  =  15,000  lb.  The  section  modulus,  Q  =  —  ; 


substituting  the  values  of  M  and  S,  Q  — 


450,000 


=  30.  From 


15,000 

Table  XIX,  page  90,  it  is  found  that  a  10"  beam  weighing  33  lb. 
per  ft.  has  a  section  modulus  of  32.3,  and  would  meet  the 
requirements.  It  is,  however,  seen  that  for  a  12"  beam, 
weighing  31£  lb.  per  ft.,  Q  =  36.7 ;  and  on  account  of  its 
greater  strength  and  less  weight,  this  beam  would  be  by  far 
the  most  economical. 

Stone  Beams. — The  strength  of  lintels,  flagstones,  etc.  may 
be  calculated  as  rectangular  beams,  except  that  it  is  usual  to 
use  a  factor  of  safety  at  least  of  10.  It  is,  however,  more  con¬ 
venient  to  use  the  formula, 

W  =  ~  X  c, 


in  which  W  =  safe  uniformly  distributed  load  in  tons 
of  2,000  pounds ; 

b  =  breadth  of  beam  in  inches ; 
d  —  depth  of  beam  in  inches ; 
l  —  span  of  beam  in  inches ; 
c  —  coefficient  taken  from  the  following  table  : 


Kind  of  Stone. 

Coefficient. 

Bluestone . 

.18 

Granite . 

.12 

Limestone  . 

.10 

Sandstone  . 

.08 

Slate  . 

.36 

Example.— A  limestone  lintel  20  in.  wide  X  14  in.  thick 
spans  a  42"  opening.  What  is  the  safe  distributed  load  ? 


120 


STRUCTURAL  DESIGN. 


b  d2 

Solution.— Substituting  values  in  the  formula,  — r—  X  c, 
W  =  20  X  lo— "  X  .10  =  9.33  tons  =  18,660  lb. 

*XjU 

If  the  load  is  concentrated  at  the  center  of  the  span,  the 
safe  load  will  be  one-half  the  safe  uniform  load. 


DESIGN  OF  RIVETED  GIRDERS. 

For  heavy  loads  and  long  spans,  plate  girders  are  substi¬ 
tuted  for  rolled  beams.  A  plate  girder  consists  of  a  web-plate, 


flange  P/arej 


rLAN&t  A  A/CL  ES. 


-  £nd  Stiffeners. 

Filler — 


f/ange  P/ate^  ^ 


EEEZEZnML 


Intermediate 
Stiffeners.  — 

Web  P/ate. 


l  owcr  flang. 


Web  Plate. 

Packing  pieces  or  fillers. 


e 


Q 


Fig.  20. 


with  stitfeners,  if  required,  and  of  the  upper  and  lower 
flanges,  as  shown  in  Fig.  20. 

Loads  upon  a  plate  girder  develop  shearing  stresses, 

resisted  by  the  web-plate, 
and  horizontal  compres¬ 
sive  and  tensile  stresses, 
resisted  by  the  upper  and 
lower  flanges.  The  usual 
cross-sections  of  plate 
girders  are  shown  in  Fig. 
21.  The  single-webbed 
girders  (a)  are  the  most 
economical  in  material,  and  the  most  accessible  for  painting 
and  inspection.  The  box  girders  (6),  however,  may  be  used 
to  advantage  where  a  wide  top  flange  is  required  for  lateral 
stiffness. 

Proportioning  Web.— The  width  of  the  web-plate  governs  the 
depth  of  the  girder,  which,  to  avoid  excessive  deflection, 


BEAMS  AND  GIRDERS. 


121 


should  not  be  less  than  TV  the  clear  span,  although  some 
authorities  permit  £>.  If  made  more  shallow,  the  sectional 
area  of  the  flanges  should  he  increased,  so  as  to  reduce  the 
stress  on  them,  and  the  deflection  in  proportion. 

The  thickness  of  web-plates  depends  upon  the  shear, 
which  is  greatest  at  the  supports.  This  thickness  must  be 
such  that  the  internal  resistance  to  shear— found  by  multi¬ 
plying  the  area  of  cross-section  of  web  by  the  safe  unit  shear¬ 
ing  stress — shall  be  equal  to  the  maximum  shear  on  the 
girder ;  that  is,  if  A  be  the  area  of  cross-section,  in  square 
inches ;  s,  the  safe  unit  shearing  stress ;  and  S,  the  maximum 
shear,  then  As  =  S;  but  as  A  is  equal  to  the  thickness  (f)  in 
inches  multiplied  by  the  net  depth  (d'),  in  inches,  td' s  =  S, 

s 

or  t  —  Hence,  the  necessary  thickness  in  inches  of  web  is 


equal  to  the  maximum  shear  divided  by  the  product  of  the  net 
depth  of  the  girder  in  inches  times  the  safe  unit  shear.  The  net 
depth  is  the  width  of  the  web  minus 
the  sum  of  diameters  of  all  rivet 
holes  in  a  vertical  line  at  the  end 
stiffeners.  The  safe  unit  shear  is 
usually  taken  at  about  f  the  safe 
horizontal  stresses;  or,  for  steel  gir¬ 
ders  in  buildings,  about  11,000  lb.  per 
sq.  in.  In  no  case  should  the  web  be 
less  than  xbb  in.  thick. 

Example. — Fig.  22  shows  the  end 
of  a  girder,  the  greatest  reaction  be¬ 
ing  120,000  lb.;  with  an  allowable 
unit  shearing  stress  of  11,000  lb., 


what  should  be  the  thickness  of  the 
web-plate? 

Solution.— The  width  of  plate 
is  48  in.,  and  there  are  13  —  rivet 

holes.  Allowing  }  in.  for  punching  each  hole,  the  net 
depth  is  48  in.  —  (J  X  13)  =  36f  in.  Applying  the  formula, 


‘  =  -Wxitooo  =  ^ in'  As  this  is  1685  lhan  * in - ,he 

latter  thickness  is  used.  * 


122 


STRUCTURAL  DESIGN. 


Stiffeners.— Web-plates,  besides  resisting  direct  vertical 
shear,  must  resist  buckling.  To  avoid  failure  by  buckling 
before  the  full  shearing  strength  of  the  plate  is  realized, 
stiffeners,  composed  of  angles,  as  shown  in  Fig.  20,  must  be 
used.  Some  engineers  require  the  use  of  stiffeners  when  the 
unit  shear  exceeds  the  ui  at  stress  allowed  by  the  following 
formula :  .  12,000 


s  = 


1  + 


d°- 


in  which 


3,000  <2 

s  —  allowable  unit  stress ; 
d  =  depth  of  girder,  between  flanges,  in  inches ; 
t  =  thickness  of  web-plate  in  inches. 

A  more  convenient  rule  provides  that  stiffeners  he  used 
when  the  thickness  is  less  than  eg  the  clear  distance  between  vertical 
legs  of  flange  angles.  For  example,  in  a  girder  with  a  f"  X  36" 
web  and  6"  X  6"  flange  angles,  the  distance  between  vertical 
legs  of  angles  is  36  —  (2  X  6)  =  24  in.;  ^  of  24  in.  =  .48,  say  £  in.; 
the  web-plates  being  but  f  in.  thick,  stiffeners  must  be  used. 

Stiffeners  should  never  be  omitted  over  the  end  supports, 
and  should  be  provided  under  all  concentrated  loads.  The 
distance  between  centers  of  intermediate  stiffeners  is  usually 
made  equal  to  the  depth  of  girder.  Under  no  condition, 
however,  should  stiffeners  be  placed  more  than  5  ft.  a"part. 

End  stiffeners  should  be  considered  as  columns  transmit¬ 
ting  the  entire  load  upon  the  web  to  the  supports.  The  size 
of  intermediate  stiffeners  is  not  usually  calculated ;  they  are 

usually  made  the  same  size 
as  the  end  ones,  or  lighter. 
Angles  used  for  stiffeners 
should  not  be  less  than  3" 
X  3"  X  tb";  on  shallow  gir¬ 
ders,  however,  with  light 
loads,  it  might  be  economical 
to  use  2^"  X  2j"  X  re"  angles; 
butsmalleronesshould  never 
be  used.  Stiffeners  should 
extend  over  the  vertical  legs  of  the  flange  angles,  being 
either  swaged  out  to  fit,  as  shown  at  (a)  and  ( b ),  Fig.  23,  or, 
preferably,  provided  with  filling  pieces,  as  shown  in  Fig.  20. 


Fig.  28. 


BEAMS  AND  GIRDERS. 


123 


Example. — Using  4  end  stiffeners  (2  each  side),  and  a  safe 
unit  compressive  stress  of  13,000  lb.,  what  size  angles  should 
be  used  for  stiffeners  of  the  girder  shown  in  Fig.  22. 

Solution. — The  required  sectional  area  is  120,000-^13,000 
=  9.23  sq.  in.;  9.23  sq.  in.  -p  4  =  2.31  sq.  in.,  the  area  required 
for  each  angle.  From  Table  XIV,  a  4"  X  4"  X  tb"  angle  has  a 
sectional  area  of  2.40  sq.  in.,  which  is  ample. 

Flanges. — The  flanges  of  a  girder— called  top  and  bottom 
chords  in  open  or  lattice  girders— include  the  flange  plates 
and  angles,  as  shown  in  Fig.  20.  Frequently,  one-sixth 
the  sectional  area  of  the  web  plate  is  included  as  part  of  each 
flange,  although,  in  many  cities,  the  building  ordinance  will 
not  allow  this  to  be  done.  If  the  sixth  is  so  included,  the 
web  should  never  be  spliced  at  the  point  of  greatest  bending, 
and  all  splices  should  be  so  designed  that,  by  proper  placing 
of  the  rivets,  the  strength  of  the  web  included  in  the  one- 
sixth  be  reduced  as  little  as  possible. 

In  a  simple  girder,  the  top  flange  is  subjected  to  compres¬ 
sion,  and  the  bottom  one  to  tension.  It  is  the  practice,  for 
economy  in  construction,  to  make  the  flanges  alike,  only 
the  lower  flange  being  calculated.  The  bottom  flange  being 
in  tension,  the  area  of  the  rivet  holes  are  deducted,  so  that 
the  net  area  at  the  point  of  least  strength  may  be  obtained. 

The  horizontal  stresses  on  the  flanges  are  resisted  by  the 
fibers  in  one  flange  acting  with  a  moment  about  the  center  of 
gravity  of  the  other.  This  moment  is  equal  to  their  total 
strength  multiplied  by  the  distance  between  centers  of 
gravity  of  the  flanges.  Thus,  Fig.  24  shows  a  plate  girder 


pin  connected  at  a,  and  a  chain  in  tension,  representing  the 
lower  flange,  at  b.  It  is  evident  that  the  reactions  tend  to 
turn  the  girder  about  a,  and  rupture  the  chain,  which  resists 


124 


STRUCTURAL  DESIGN. 


this  tendency  with  a  lever  arm  d  equal  to  the  distance 
between  the  centers  of  gravity  of  the  flanges.  The  depth  is, 
in  practice,  however,  usually  taken  to  be  the  depth  of  the  web. 

To  find  the  net  area  of  the  lower  flange,  let  3IX  be  the 
resisting  moment  in  foot-pounds ;  M,  the  bending  moment  in 
foot-pounds ;  s,  the  allowable  unit  tensile  stress ;  a,  the  net 
area  of  flange  in  square  inches ;  and  d,  the  depth  of  girder  in 

feet ;  then  sXaXd  —  Mu  which  must  be  equal  to  M ;  from 
M 


which  a  = 


sXd 


Rule. — The  net  sectional  area  of  the  lower  flange  of  a  plate 
girder  is  equal  to  the  greatest  bending  moment  in  foot-pounds 
divided  by  the  product  of  the  allowable  unit  tensile  stress  in  pounds 
and  the  depth  of  the  girder  in  feet. 

In  proportioning  the  flanges,  the  sectional  area  of  the 
flange  plates  should  equal,  approximately,  that  of  the  flange 
angles.  This  is  not  possible  in  heavy  work,  and  the  best  that 
can  be  done  is  to  use  the  heaviest  sections  obtainable  for  the 
flange  angles. 

Example.— A  steel  girder  is  6  ft.  deep,  and  80  ft.  span,  and 
the  load  3,000  lb.  per  lineal  foot,  (a)  What  net  flange  area 
is  required,  using  a  safe  unit  tensile  stress  of  15,000  lb.  per 
sq.  in.?  (b)  Of  what  size  sections  should  the  flange  be  made? 

Solution.— (a)  The  entire  load  is  80  X  3,000  =  240,000  lb. 
From  Table  XXVI,  page  113,  the  bending  moment  is 

WL  240,000  X  80 


3-  /4x£  Hange  P/otes. 


M= 


Ang/ej. 


8  t8 
The  net  flange  area 
M  2,400,000 


=  2,400,000  ft. -lb. 


a  = 


=  26.6  sq.  in. 


Fig.  25. 


sXd  15,000  X  6 

(5)  Assume  the  section  shown  in  Fig. 
25.  The  area  of  a  6"  X  6"  X  t"  angle 
being,  approximately,  7  sq.  in.,  the  sec¬ 
tional  area  of  the  flange  is, 

Two  6"  X  6"  X  i"  angles  =  7X2  =  14.00  sq.  in. 
Three  14"  X  TV'  plates  =  14  XT7SX3  =  18.37  sq.  in. 

Total  =  32.37  sq.  in. 

From  the  total  area  deduct  the  metal  cut  out  for  rivet 
holes,  which,  taken  as  |  in.  larger  than  the  rivet,  are  1  in.  in 


BEAMS  AND  GIRDERS. 


125 


diameter.  The  web  is  not  considered  in  the  flange  section. 
The  areas  deducted  are,  therefore, 

Four  1"  holes  through  \n  metal  =  2£  sq.  in. 

Two  1"  holes  through  1£§"  metal  =  3£  sq.  in. 


Total  =  6|  sq.  in. 


The  net  area  of  the  flange  is  32.37  —  6.37  =  26  sq.  in.,  which, 
although  a  little  less  than  the  net  area  required,  26.6  sq.  in., 
could  be  used. 

Length  of  Flange  Plates. — The  bending  moment  on  a  simple 
beam  varies  throughout  the  length  ;  and,  to  design  girders 
economically,  the  net  flange  area  should  vary  with  the  bend¬ 
ing  moment.  This  condition  is  fulfilled  by  using  flange  plates 
of  different  lengths,  each  extending  only  as  far  as  needed  to 
provide  the  net  section  required.  It  is  good  practice  to  con¬ 
tinue  the  inner  plate  the  entire  length  of  the  girder,  in  order 
to  stiffen  it  laterally.  The  lengths  of  flange  plates  in  girders 
uniformly  loaded  may  be  obtained  approximately  by  the 
formula : 

1^  =  2  +  L 


J-j'x/a’p/ates. 
H/vetsjdio\ 


■jxsyy 

Angles. 


L\  being  the  required  length  of  the  plate  in  feet ;  L,  the  length 
of  girder  in  feet ;  a,  the  net  sectional  area  of  all  plates  to  and 
including  the  plate  in  question,  beginning  with  outside  one  ; 
and  A,  the  total  flange  area.  The  2  ft.  is  added  to  allow  for 
riveting. 

Example. — Fig.  26  shows  a  flange  section  of  a  girder. 
The  span  being  60  ft.,  what  should  be  the 
length  of  each  flange  plate? 

Solution.— Area  of  a  5"  X  5"  X  £' "‘angle 
(see  Table  XIV,  page  85)  is  7.11  sq.  in. 

Area  of  each  plate  is  f  in.  X  12  in.  =  4.5 
sq.  in.;  the  rivet  holes  are  £  +  £  =  £  in., 
and  the  area  cut  out  by  a  hole 
through  a  f"  plate  is  .328  sq.  in.;  hence,  the  net  area  of  each 
plate  is  4.5  sq.  in.  —  (.328  sq.  in.  X  2)  =  3.844  sq.  in.;  or,  for  3 
plates,  3.844  X  3  =  11.532  sq.  in.  The  net  area  of  the  two 
angles  is  (7.11  sq.  in.  X  2)  —  (.656  X  4)  =  11.596  sq.  in.  There¬ 
fore,  the  net  area  of  flange  will  be  11.532  +  11.596  =  23.128 
sq.  in. 


Fig.  26. 


126 


STRUCTURAL  DESIGN. 


By  the  formula,  the  leng  th  of  outside  plate 

hi  =2  +  60  A  /  =  26.42,  say  26  ft.  6  in. 

\  23.128 

Similarly,  the  length  of  the  intermediate  plate 

Lx  —  2  +  60  =  36.56  ft.,  say  36  ft.  6  in. 


The  inner  plate  is  continued  the  entire  length  of  the 
girder,  so  as  to  stiffen  it  laterally. 

Fig.  27  shows  a  graphical  method  of  finding  the  lengths  of 
flange  plates  for  a  girder  carrying  any  number  of  concen¬ 
trated  loads.  Lay  off 
a  b  to  any  scale,  equal 
to  the  span,  and  locate 
on  it  the  point  of  appli¬ 
cation  of  each  load,  as 
c,  d,  and  e.  Having  cal¬ 
culated  the  bending 
moment  under  each 
load,  lay  it  off,  to  a  con¬ 
venient  scale,  on  the  corresponding  perpendicular  to  a  b, 
through  c,  d,  and  e,  as  cf,  d  g,  and  e  h.  Draw  the  lines  af,f  g, 
gh,  and  hb.  Divide  eh,  the  line  representing  the  greatest 
bending  moment,  into  as  many  equal  parts  as  there  are  square 
inches  in  the  net  section  required.  (For  a  method  of  dividing 
a  space  into  equal  parts,  see  Geometrical  Draining,  page  55.) 
Take  er  equal  to  as  many  parts  as  there  are  square  inches  in 
the  net  sectional  area  of  flange  angles;  also,  rs  equal  to  net 
area  of  the  first  plate,  etc.  Draw  parallels  to  a  b  through  r,  s,  t, 
etc.  Make  ik  equal  to  ah  ;  where  ik,  etc.  intersects  a  f  and 
b  li,  erect  perpendiculars  p  l  and  q  m,  etc.  Then  l  m,  measured 
to  same  scale  as  a  b,  is  the  length  of  the  first  flange  plate ;  n  o, 
that  of  the  second,  etc.  The  lengths  thus  found  should  be  in¬ 
creased  1  ft.  at  each  end,  to  allow  for  riveting. 

The  lengths  of  plates  for  uniformly  loaded  girders  may  be 
similarly  found.  Having  calculated  the  maximum  bending 
moment,  lay  it  off  to  scale,  perpendicular  to  the  middle  of 
die  span.  The  curve  representing  the  bending  moment  is  in 
ihis  case  a  parabola,  and  may  he  drawn  through  the  point 


BEAMS  AND  GIRDERS. 


127 


just  named  and  the  ends  of  the  span,  by  the  method  given  in 
Geometrical  Drawing  on  page  58.  The  remainder  of  the  work 
is  like  that  shown  in  Fig.  27. 

Rivet  Spacing.— Enough  rivets  must  be  placed  in  the  end 
stiffeners  of  girders  to  transmit  the  shear  to  the  web.  For 
example,  100,000  lb.  is  the  reaction  on  a  girder  constructed  as 
in  Fig.  22  ;  the  web  is  f  in.  thick,  the  rivets  £  in.  diam. 
The  allowable  unit  bearing  value  being  15,000  lb.  (by 
Table  XXIX,  page  131),  the  ordinary  bearing  of  a  plate  on  a 
j"  rivet  is  4,920  lb.;  adding  |  because  the  plate  is  web  bearing, 
gives  6,560  lb.  Since  the  double  shearing  value  of  the  rivet  is 
greater  than  the  web-bearing  value  of  the  plate,  6,560  lb. 
must  be  taken  as  the  resistance  of  one  rivet.  Then  the  number 
of  rivets  required  in  the  two  pairs  of  angles  is  100,000  g-  6,560 


=  15.2,  say  16,  or  8  rivets  in  each  pair.  Rivets  in  intermediate 
stiffeners  are  usually  spaced  the  same  as  in  end  stiffeners, 
their  spacing  not  being  calculated.  No  rivets  in  stiffeners 
should  be  spaced  more  than  6  in.  apart,  or  more  than  16  times 
the  thickness  of  the  angle  leg. 

As  the  shear  increases  from  the  point  of  greatest  bending 
towards  the  supports,  the  number  of  rivets  j>laced  in  the 
vertical  legs  of  the  flange  angles,  to  resist  their  tendency  to 
slide  on  the  web,  must  also  increase  as  the  supports  are 
approached.  The  horizontal  stress,  per  inch  of  length,  which 
is  transmitted  from  the  web  to  the  flange  at  any  point,  is 
equal  to  the  maximum  shear  at  any  point  divided  by  the 
depth  of  the  girder  in  inches. 

For  example,  in  the  girder  shown  in  Fig.  28,  the  shear  at  a 
is  Ri,  or  100,000  lb.;  at  5,  it  is 
100,000  lb.  —  (5,000  lb.  X  4)  = 

80,000  lb.,  at  c,  60,000  lb.,  etc. 

The  horizontal  stress  per  inch 
of  length  at  a  is  100,000  (4 

X  12)  =  2,083 lb.;  at  6,  80,000  -f-  48 
=  1,667  lb.;  at  c,  60,000  ^48  = 

1,2501b.;  at  d,  833  lb.,  etc.  Using 
V  rivets,  the  safe  bearing  value 
of  each  is  6,560  lb.  At  a,  the  stress  being  2,083  lb.  per  inch  of 
run,  the  rivets  should  be  placed  6,560  h- 2,083  =  3.14  in.  center 


Uniform  Load  5000  lb, 
per  / i'nea/  foot. 


Fig.  28. 


128 


STRUCTURAL  DESIGN. 


to  center;  at  b,  6,560^-1,667  =  3.93  in.;  at  c,  6,560 -i- 1,250  = 
5.24  in.;  at  d ,  6,560-^833  =  7.87  in.  In  practice,  rivets  are 
spaced  alike  in  both  flanges;  and  as  6  in.  is  the  greatest 
allowable  pitch  in  a  compression  member,  further  calcula¬ 
tion  is  needless.  The  rivet  spacing  from  a  to  b  is,  then,  3£  in.; 
b  to  c,  4  in.;  c  to  d,  5i  in.;  beyond  d,  as  the  theoretical  pitch 
is  more  than  6  in.,  the  6-in.  pitch  should  be  used. 

At  the  ends  of  each  flange  plate,  sufficient  rivets  must  be 
used,  spaced  2^  to  3  in.  on  centers,  to  transmit  the  allowable 
stress  on  the  net  section  of  the  plate  to  the  adjacent  mem¬ 
bers.  The  remaining  rivets  should  be  spaced  the  greatest 
allowable  pitch  for  a  compression  member,  namely,  16  times 
the  thickness  of  the  thinnest  outside  plate — provided  the 
pitch  does  not  exceed  6  in.  For  example,  in  a  f"  X  12"  flange 
plate,  after  deducting  the  area  of  two  1"  holes  (£"  rivets  + 
i"),the  net  sectional  area  is  3f  in.  Assuming  the  safe  unit 
fiber  stress  at  15,000  lb.,  3.75  in.  X  15,000  =  56,250  lb.,  strength 
of  plate.  The  safe  value  of  each  rivet  in  this  case  will  be 
taken  at  5,410  lb.;  then  the  number  required  in  each  end  of 
the  plate  is  56,250  -e-  5,410  —  10,  say  5  each  side  of  the  web,  and 
they  should  be  spaced  from  2\  to  3  in.  on  centers.  In  splicing 
the  lower  flange  angles,  which  are  in  tension,  enough  rivets 
should  be  placed  therein  to  equal  in  resistance  that  of  the  net 
section  of  the  angles.  In  splicing  the  top  angles,  since  they 
are  in  compression,  only  enough  rivets  need  be  used  to 
securely  hold  them  in  abutting  position. 


STRENGTH  OF  RIVETS  AND  PINS. 


RIVETS. 

In  proportioning  riveted  joints,  the  friction  between  the 
plates  cause.d  by  the  clamping  effect  of  the  rivets  is  neglected. 
Hence,  a  riveted  joint  may  fail  in  two  ways,  namely,  by  the 
shearing  of  the  rivets,  and  by  the  crippling  or  crushing  of  the 
metal  in  the  member  around  the  rivet  hole.  It  is  necessary 
therefore,  in  designing  a  riveted  joint,  to  consider,  besides  the 
shearing  of  the  rivets,  the  bearing  value  of  the  plates  or  rolled 
sections. 


STRENGTH  OF  RIVETS  AND  PINS. 


129 


The  strength  of  a  riveted  joint  also  depends  upon  the  dis¬ 
tribution  of  the  members  connected,  and  the  location  of  the 
rivets ;  that  is,  whether  the  rivets  are  in  single  or  double  shear, 
and  the  members  connected  in  ordinary  or  web  bearing. 

A  rivet  may  be  in  single  shear,  as  at  (a),  or  in  double  shear  as 
shown  at  ( b ),  in  Fig.  29.  At  (a)  the  tendency  is  to  shear  the 
rivet  along  the  line  a  b, 
and  the  strength  of  the 
rivet  is  equal  to  its  sec¬ 
tional  area  multiplied  by 
the  shearing  strength  of  the 
material  composing  it.  At 
(b)  the  tendency  is  to 
shear  the  rivet  along  the 
lines  a  b  and  cd ;  hence, 
the  strength  of  the  rivet 
in  this  case  is  twice  that  of  the  former,  and  is  equal  to  twice 
the  sectional  area  of  the  rivet,  midtiplied  by  the  shearing  strength 
of  the  material  in  the  rivet. 

The  plates  or  structural  sections  composing  a  joint  tend 
to  fail  or  cripple,  as  at  a,  Fig.  30.  Hence,  the  bearing 

strength  of  a  plate  is  equal  to 
the  thickness  of  the  plate  multi¬ 
plied  by  the  diameter  of  the  rivet 
and  this  product  by  the  bearing 
strength  of  the  material  compo¬ 
sing  the  plates  or  rolled  sec¬ 
tions.  Where  the  plate  is 
situated,  as  at  (6),  Fig.  29,  between  two  outside  plates,  the 
central  plate  is  said  to  be  subjected  to  web  bearing,  and  it  is 
usual  to  consider  the  value  of  this  plate,  in  resisting  bearing, 
to  be  a  third  higher  than  in  ordinary  bearing,  as  at  (a). 

The  most  reliable  test  of  steel  and  iron  is  the  tensile,  and 
the  shearing  and  bearing  values  are  deduced  from  it.  Com 
servative  practice  takes  shearing  values  for  high-grade  iron 
and  steel  at  £  of  the  tensile  strength  of  the  material,  and  the 
ordinary  bearing  value  at  li  times  the  tensile,  while  web  bear¬ 
ing  is  taken  at  twice  the  tensile  strength,  On  this  basis  the 
following  table  is  formed : 


Fig.  29. 


130 


STRUCTURAL  DESIGN. 


TABLE  XXVIII. 

Allowable  Shear  and  Bearing  Values. 


Pounds  per  Square  Inch. 

Character  of 

Rivets. 

Work. 

\ 

Shearing. 

Ordinary 

Bearing. 

Web 

Bearing. 

Iron 
rivets  1 

Railroad  bridges 

6,000 

12,000 

16,000 

Iron 

rivets 

Highway  bridges 
and  buildings 

7,500 

15,000 

20,000 

Steel 
rivets  I 

Railroad  bridges 

7,500 

15,000 

20,000 

Steel  ' 
rivets  _ 

Highway  bridges 
and  buildings 

9,000 

18,000 

24,000 

It  is  therefore  important,  in  designing  riveted  joints,  to 
determine  whether  the  shearing  strength  of  the  rivets  or  the 
bearing  values  of  the  plates  is  the  stronger,  and  to  proportion 
the  joint  accordingly. 

Table  XXIX  gives  the  shearing  and  bearing  values  for  the 
principal  sizes  of  rivets  and  plates  used  in  steel  construction. 

The  greatest  economy  in  material  is  obtained  when  the 
net  area  of  the  plates  or  members  joined  is  the  greatest 
possible ;  that  is,  when  the  percentage  or  ratio  existing 
between  the  net  section  and  the  gross  section  is  as  great  as 
can  be.  It  is  usual,  in  proportioning  riveted  work,  where 
the  rivets  are  driven  by  hand  in  the  field,  to  increase  the 
number  of  rivets  25  or  50  percent,  to  allow  for  faulty  riveting. 

It  has  previously  been  said  that  rivets  fail  by  shearing ; 
they  are,  however,  in  rare  instances  liable  to  fail  by  bending. 
This  occurs  only  when  the  rivets  are  long  and  it  is  impossible 
to  drive  them  enough  to  have  them  upset  sufficiently  to  fill 
the  holes.  In  such  case  the  only  remedy  is  to  so  design  the 
joint  as  to  lessen  the  grip  of  the  rivet,  or  increase  the  number 
of  rivets,  and  consequently  reduce  the  tendency  to  bending. 
Rivets  are  never  proportioned  to  withstand  flexure. 


STRENGTH  OF  RIVETS  AND  PINS. 


131 


TABLE  XXIX. 

Shearing  and  Bearing  Values  of  Rivets. 


Diam¬ 
eter  of 
Rivet. 
Inches. 


A 

8 

1. 

9 

A 

8 

i 

2_ 

8 

1 


Diam¬ 
eter  of 
Rivet. 
Inches. 


_1 

9 

I 

x 

8 

1 


Diam¬ 
eter  of 
Rivet. 
Inches. 


I 

L 

9 

I 

I 

7 

8 

1 


Single 
Shear 
at  6,000 
Lb.  per 
Sq.  In. 

Bearing  Value  at  12,000  Lb.  per  Sq.  In.  for 
Different  Thickness  of  Plate  in  Inches. 

1 

4 

5 

TB 

A 

8 

7 

16 

1 

9 

9 

TB 

1 

660 

1,180 

1,840 

2,650 

8,610 

4,710 

1,120 

1,500 

1,860 

2,250 

2,630 

3,000 

1,880 

2,320 

2,810 

3,280 

3,750 

2,250 

2,790 

3,370 

3,940 

4,500 

3.250 
3,940 
4,590 

5.250 

3,720 

4,500 

5,250 

6,000 

5,060 

5,910 

6,750 

6,560 

7,500 

Single 
Shear 
at  7,500 
Lb.  per 
Sq.  In. 

Bearing  Value  at  15,000  Lb.  per  Sq.  In.  for 
Different  Thickness  of  Plate  in  Inches. 

1 

4 

6 

«TB 

A 

8 

7 

IB 

1 

9 

TS 

1 

830 

1,470 

2,300 

3,310 

4,510 

5,890 

1,410 

1,880 

2,340 

2,810 

3,280 

3,750 

2,340 

2,930 

3,520 

4,100 

4,690 

2,810 

3,520 

4,220 

4,920 

5,620 

4,100 

4,920 

5,740 

6,560 

5,630 

6,560 

7,500 

6,330 

7,380 

8,440 

8,200 

9,380 

Single 
Shear 
at  9,000 
Lb.  per 
Sq.  In. 

Bearing  Value  at  18,000  Lb.  per  Sq.  In.  for 
Different  Thickness  of  Plate  in  Inches. 

1 

4 

5 

TB 

A 

8 

7 

1 

9 

9 

TB 

* 

990 

1,770 

2,760 

3,970 

5,410 

7,060 

1,680 

2,250 

2,790 

3,370 

3,940 

4,500 

2,820 

3,480 

4,210 

4,920 

5,620 

3,370 

4,180 

5,050 

5,910 

6,750 

4.870 
5,910 
6,880 

7.870 

5,580 

6,750 

7,870 

9,000 

7,590 

8,860 

10,120 

9,840 

11,250 

132 


STRUCTURAL  DESIGN. 


Example. — Fig.  31  shows  the  riveted  joint  for  a  tension 
member.  The  allowable  stress  for  the  rivets  in  single  shear  is 

7,500  lb.  per  sq.  in.,  and  the 
l‘t2fWrt iron  Bon  safe  bearing  and  tensile  values 
of  the  wrought-iron  bars  15,000 


„  ~  - - re r" 

i<tiaJTiret\ 
jUtxl 


9^ 


gxNWrt  Iron  Bar  nflTrtlronBar. 

Fig.  31. 


and  12,000  lb.  per  sq.in.,  respect¬ 
ively;  what  will  be  the  safe 
resisting  strength  of  the  mem¬ 
ber  at  the  connection  ? 


Solution. — Determine  whether  the  shear  of  the  rivets, 
the  bearing  value  of  the  bars,  or  the  tensile  strength  of  the 
members  connected,  is  the  strongest.  The  combined  sections 
of  bars  a  and  c  are  equal  to  that  of  b.  The  safe  tensile 
strength  of  members  connected  is  equal  to  strength  of  net 
section  of  the  bar  b,  obtained  by  deducting  from  the  gross 
section  of  b  the  area  of  metal  cut  out  for  rivet  holes.  The  rivet 
hole  is  considered  as  }  in.  larger  than  the  rivet ,  to  compensate  for 
the  deterioration  of  the  metal,  due  to  punching.  The  gross  sec¬ 
tion  is  equal  to  £  in.  (thickness)  X  2  in.  (width)  =  1.25  sq.  in. 
The  section  of  metal  cut  out  for  the  rivet  hole  is  equal  to 
.625  in.  X  .875  in.  (diameter  of  rivet  hole)  =  .5468  sq.  in.;  the 
net  section  of  the  bar  is  therefore  equal  to  1.25  sq.  in.  —  .5468 
sq.  in.,  or  .7032  sq.  in.  The  safe  tensile  strength  of  bar  b  is 
eqmal  to  .7032  sq.  in.  X  12,000  lb.  (safe  tensile  strength  per  sq. 
in.  of  material)  =  8,438  lb.,  which  is  also  the  combined 
strength  of  the  bars  a  and  c. 

In  Fig.  31  it  is  evident  that  the  two  f"  rivets  are  in 
double  shear  along  the  lines  e  d  and  b  a,  but,  by  referring  to 
Table  XXIX,  it  will  be  seen  that  the  safe  bearing  value  of  a 

rivet  upon  a  plate  is  2,810  lb.,  which  is  less  than  the  safe 
shearing  stress  of  the  rivet,  and  is  therefore  the  one  to  be 
used.  The  bearing  value  of  the  V  rivet  upon  the  §"  bar  c  is 
greater  than  the  shearing  stress  of  the  rivet ;  therefore,  in  this 
case  the  shear  of  the  rivet  should  be  taken  as  its  resistance. 
The  safe  resistance  of  the  i"  rivets  is  then  as  follows : 

Shear  of  two  V'  rivets  on  line  e  d  —  3,310  X  2  =  6,620  lb. 

Bearing  value  of  two  rivets  on  i"  plate  2,810  X  2  =  5,620  lb. 

Total  =  12,240  lb. 


STRENGTH  OF  RIVETS  AND  PINS. 


133 


To  this  add  the  safe  shearing  stress  of  the  %"  rivet,  which  is 
2,300  lb.,  or  less  than  its  safe  hearing  value  against  the  %"  bar. 
Thus,  12,240  +  2,300  =  14,540  lb.,  the  safe  resistance  of  the 
rivets  to  shear,  and  the  plates  or  bars  to  crippling.  From 
these  results,  it  is  seen  that  the  net  section  of  the  bars  is 
weaker  than  the  connection  ;  hence,  the  safe  strength  of  the 
tension  member  is  8,438  lb.,  the  strength  of  bar  b,  or  the  com¬ 
bined  strength  of  bars  a  and  c. 

Pitch  of  Rivets. — The  least  distance  from  center  to  center 
of  rivets,  or  the  pitch,  should  not  be  less  than  3  times  the  diam¬ 
eter  of  the  rivet.  If  the  members  are  in  tension,  the  greatest 
pitch  should  not  be  more  than  30  times  the  thickness  of  the 
thinnest  outside  plate  or  member.  If  the  members  are  in 
compression,  the  pitch  should  not  be  more  than  16  times  the 
thickness  of  the  thinnest  outside  plate  or  member.  The  pitch 
should  never  be  greater  than  6  in.,  except  where  the  rivets 
are  set  zigzag,  or  staggered,  in  which  case  the  pitch  should  not 
be  more  than  6  in.  in  a  staggered  line.  The  distance  from  the 
end  of  a  plate  to  the  center  of  a  rivet  should  not  be  less  than 
the  thickness  of  the  plate  plus  the  diameter  of  the  rivet  plus 
s  in.  The  distance  from  the  center  of  a  rivet  to  the  side  of 
the  plate  should  not  be  less  than  one-half  the  thickness  of  the 
plate  plus  one-half  the  diameter  of  the  rivet  plus  £  in. 

The  sizes  of  rivets  most  commonly  used  in  building  con¬ 
struction  are  £  in.  and  |  in.  diameter ;  |  in.  are  sometimes 
used  in  connections  where  there  is  but  little  strain.  For 
economy,  there  should  be,  in  any  structure,  as  few  different 
sizes  of  rivets  as  possible. 


STRENGTH  OF  PINS. 

In  proportioning  pin-connected  joints,  the  shear  of  the  pin 
and  the  bearing  value  of  the  connected  plates  should  be  con¬ 
sidered  in  the  same  manner  as  was  riveted  joints.  Pins,  how¬ 
ever,  are  subjected  to  bending  stresses  that  are  neglected  in 
riveted  work ;  pins  should  always  be  proportioned  to  with¬ 
stand  such  bending  stresses.  Round  pins  should  be  con¬ 
sidered  as  beams  having  a  solid  circular  cross-section.  The 
bending  moment  in  inch-pounds  should  be  determined  in  a 
similar  manner  as  for  any  beam  (see  pages  107  to  120),  and 


134 


STRUCTURAL  DESIGN. 


I 


10000  lb. 


lOOOO  lb 


nr- 


- - > 

1 

« 

JL 


Fig.  32. 


the  resisting  moment  of  the  section  obtained,  which  may  be 
calculated  (see  page  114),  or  obtained  from  Table  XXX, 
which  also  gives  the  shearing  and  bearing  values  for  differ¬ 
ent  size  pins. 

Example. — What  size  pin  will  be  required  to  resist  bend¬ 
ing  in  the  connection  shown  in  Fig.  32? 

Solution.— The  bending  moment  is  10,000  lb.  X  6  in. 
=  60,000  in. -lb. 

The  proper  size  pin  having  the  required  resisting  moment 
may  be  obtained  from  Table  XXX,  page  137,  or  calculated 

thus  :  The  section 
modulus  for  a 
solid  cylindrical 
section  is,  accord¬ 
ing  to  Table  XII, 
page  83,  .0982  d3. 
Since  d ,  the  diam¬ 
eter  of  pin,  must 
be  assumed,  try  31 
in.  The  section  modulus  is  .0982  X  31  X  31  X  31,  or  4.21.  Then, 
as  the  safe  resisting  moment  of  any  beam  equals  the  section 
modulus  multiplied  by  the  safe  stress  of  the  material  (see 
page  114),  and  assuming  that  the  safe  working  stress  of  the 
material  in  the  pin  is  15,000  lb.  per  sq.  in.,  the  resisting  mo¬ 
ment  is  4.21  X  15,000  =  63,150  in. -lb.  Since  the  safe  resisting 
moment  must  equal  or  exceed  the  bending  moment  (see 
page  108),  a  pin  31  in.  in  diameter  will  be  sufficient  to  resist 
the  bending' Stresses. 

Where  the  lines  of  action  of  the  stresses,  in  several  mem¬ 
bers  connected  at  a  common  joint  by  a  pin,  are  inclined  to 
one  another,  as  at  (a),  Fig.  33,  the  stresses  in  the  oblique 
members  should  be  resolved  into  their  vertical  and  horizontal 
components  (see  page  141).  Having  found  these  forgll  the 
forces  acting  upon  the  pih,  the  greatest  bending  moment  due 
to  all  the  vertical  components,  and  that  due  to  the  horizontal 
components,  should  be  obtained.  Then,  by  adding  the 
squares  of  these  two  amounts  together  and  taking  the  square 
root  of  the  result,  the  greatest  resultant  bending  moment 
will  be  found. 


STRENGTH  OF  RIVETS  AND  PINS. 


135 


Example. — Find  the  greatest  resultant  bending  moment 
upon  the  pin  shown  at  (a),  Fig.  33. 

Solution.— Draw  accurately  the  frame  diagram,  as  at  (b), 
Fig.  33,  in  which  the  full  lines  represent  the  direction  of  the 
members  assembled  at  the  joint.  Lay  off  to  some  convenient 


136 


STRUCTURAL  DESIGN. 


scale  upon  c  d,  a  distance  that  will  represent  the  stress  in  that 
member ;  then,  by  the  principle  of  the  parallelogram  of  forces, 
db  will  be  the  horizontal,  and  de  the  vertical,  component  of 
the  stress  in  c  d.  Likewise,  draw  the  horizontal  and  vertical 
components  of  the  stresses  in  the  members  c  a  and  c  h.  Since 
the  member  ce  is  horizontal,  it  will  have  no  vertical  com¬ 
ponent.  The  vertical  and  horizontal  components  of  all  the 
stresses  in  the  oblique  members  may  be  obtained  by  scaling 
the  lines  which  represent  them.  Since  all  the  members 
except  the  right-hand  oblique  one  are  in  pairs,  one-half  of 
each  stress  will  be  carried  on  each  side  of  the  center  line. 

Having  obtained  the  amounts  of  the  horizontal  and 
vertical  components,  the  diagrams  (c)  and  (d)  may  be  drawn. 
Care  must  be  exercised  to  see  that  all  the  forces  upon  one 
side  of  the  pin  are  equal  to  those  upon  the  other ;  otherwise, 
the  joint  would  not  he  in  equilibrium,  and  would  tend  to 
move  in  the  direction  of  the  greater  force.  The  diagram  (c) 
shows  the  horizontal  components  of  all  the  forces,  the  bend¬ 
ing  moment  due  to  which  is  obtained  as  follows:  (For 
bending  moment  see  page  111.) 

22,050  lb.  X  5  in.  =  110,250  in.-lb. 

deduct,  3,000  lb.  X  3  in.  =  9,000  in.-lb. 

15,000  lb.  X  4  in.  =  60,000  in.-lb.  69,000  in.-lb. 

Total  horizontal  bending  moment  =  41,250  in.-lb. 

From  the  diagram  (d)  of  all  the  vertical  components  the 
bending  moment  due  to  them  is  obtained  thus  : 

1,800  lb.  X  5  in.  =  9,000  in.-lb. 

5,150  lb.  X  3  in.  =  15,450  in.-lb. 

Total  vertical  bending  moment  =  24,450  in.-lb. 

The  resultant  bending  moment  is,  then  : 

]/  41,2502  +  24,4502  =  47,900  in.-lb. 

From  Table  XXX,  page  137,  using  a  safe  unit  stress  of  15,000 
lb.,  it  will  be  seen  that  a  pin  which  is  3T3B  in.  in  diameter  has  a 
resisting  moment  of  47,670  in-lb.,  which,  while  scant,  will  do. 

If  the  pin  is  designed  to  resist  bending,  it  is  seldom  neces¬ 
sary  to  consider  the  shear.  The  bearing  values  are  found  the 
same  as  for  rivets,  and  are  given  in  Table  XXX. 


Shearing  and  Bearing  Values  and  Maximum  Resisting  Moments  of  Pins. 


STRENGTH  OF  RIVETS  AND  PINS.  137 


Shearing 

Values. 

At  11,250 
Lb.  per 
Sq.  In. 

oooooooooooooooooo 
OOOOOOOOOIOOOOOOOOO 
dddCO  lO  CO  CO  CC^HOHOOKMOOO 

oo  lo  co  cf  cf  co  co  oT o  rd  cT  aT  oT  id  o'  id  go 

H(NCO^iOCOt^COO(NCOCOCOOiOOOOH 
t— 1  rH  i— 1  rH  i—i  Cl  d  Cl  CO  CO 

At  9,000 
Lb.  per 
Sq.  In. 

oooooooooooooooooo 

OOiO^OOOOOOOOOOOOOOO 

co  ci^  10  co  ©  ©  ©^  oo  io  r-^  ©  cowcqoqo 

^  o'  CO  co"  Cl  tH  r-T  r-T  CO  co"  cT  i  o"  r-T  I'-"  -f  -t" 

HCKMCOO'iOCNCOCOCOiOCOCl^iO 
HHHHddClCl 

At  7,500 
Lb.  per 
Sq.  In. 

oooooooooooooooooo 

lOOOOOO>OlOOOlOOOOiOOO'0 
iHOOiH<N©  lO  00  GO^COHCO^  O  O  rH  O  OO^ 

cf  co  cf  co  id' cl  o" aT oT o" th" cf  co  o"  o" r-"  cd cf 

HHddCO^iOiOCOOOOHdriU^CCOH 

HHHHHdd 

Bearing  Values  for  1  Inch 
Thickness  of  Plate. 

At  18,000 
Lb.  Per 
Sq.  In. 

oooooooooooooooooo 

OOOOOOOOOOOLOOiOLOiOiOO 
©  i>  00  c^i>  © 

io"  o"  Tf^  erf  co"  cd  cf  r-T  r-T  o"  ©"cdcdr^f  co"  r-T  id  cc" 

dCOCOCO^^iOiOCOcOI^NCOGOOOOO 

H  H  H 

At  15,000 
Lb.  Per 
Sq.  In. 

oooooooooooooooooo 

oooooooooooooooooo 

(OCOH«XOMH®fflCOH<O^HtO  T*^rH_0_ 
rH  LO^dC'f  o'o'-f' r-t  lO  O  lO  o'co'o"-f  ocTo 
MCl(NMM^l'4'^i0i0inO®1^00  00C001 

At  12,000 
Lb.  Per 
Sq.  In. 

oooooooooooooooooo 

oooooooooooooooooo 

Cl  Cl  Cl  (Cl  Cl  (Cl  Cl  <N  Cl  Cl  Cl  1C  iC  iO_iq_UO  lO  o^ 

i'.’  o’  co  co  o  ci  ire cc  r-i-ft'cf ire'odH  t~  o’  cf 

!-H(MCJ(MC)COCOCOHtlHjlrt<iOiOiOOOlri^ 

Maximum  Resisting 
Moment. 

S  =  22,500 
Lb.  Per 
Sq.  In. 

OOOOOOOOOOOOOOOOOOO 

UlrtiOrlMOffiOCOriaOOOOOOO 

iO(OOHC1050iH30t'NOiO®OH01H 

co  o' to  os'  r-T  ci'io’rH  o'  o  nji'ire’  od  o'  co  co  t--’ 

THHC'ICO'it  lOl'OOrtCOOOHiO-HCK -f  1- 

S  =  18,000 
Lb.  Per 
Sq.  In. 

oooooooooooooooooo 
HODHCOCOOC'I'OIONWIS  OOOO  o  o 

<n  -cf  oo  rf  ire  <m  t'  cqt^u^oqoi_oot^H^o  co  i> 

HHNM^lOt'COO^t'ONHiOW 
rH  rH  rH  Cl  Cl  CO  CO  CO 

S  =  15,000 
Lb.  Per 
Sq.  In. 

oooooooooooooooooo 

NKOOHbHNOHOOOOOOQO 
COOtr  rf  MlOCOtO  t-^OOCOCO  1>  OJ^rH  CO^i-q 
r^jrToiOrH'cQ't^'frOcocyrcoioocoicicocq 

HHClCICOcJlOt'CCCl^t'CCgrH 
rH  rH  rH  <M  <N  Cl  CO 

•satpui  -uid:  | 

JO  J3J8TXn}l(J  !  THHHOC'lC'lC^COCOWCOTfT#(rt<iOiOiO«5 

138  STRUCTURAL  DESIGN. 

BOLTS  AND  TENSION  BARS. 

The  strength  of  bolts  in  resisting  shear  and  bending  may 
be  analyzed  similarly  to  rivets  and  pins.  When  bolts  or 
round  bars  threaded  at  the  end  are  subjected  to  tensile  stress, 
they  tend  to  break  at  the  weakest  section,  which  is  at  the 
root  of  the  screw  thread.  In  order  to  make  the  threaded  part 
equal  in  strength  to  that  of  the  body  of  the  rod,  the  end  is 
sometimes  upset ,  so  that  the  diameter  at  the  root  of  the  thread 
will  equal  that  of  the  body.  Upsetting,  however,  requires 
more  smith  work,  the  cost  of  which  will  likely  be  more  than 
that  of  the  additional  material  required  to  increase  the  size 
enough  to  make  upset  ends  unnecessary. 

•  The  following  table  (XXXI)  gives  the  principal  dimen¬ 
sions  for  U.  S.  standard  screw  threads  and  nuts,  and  the  area 
at  the  root  of  thread  of  any  usual  size  rod.  The  strength  of 
any  tension  rod  may  be  found  by  multiplying  this  area  by  the 
tensile  strength  of  the  material. 

Example. — Required,  the  size  of  a  threaded  round  tension 
rod,  to  sustain  a  stress  of  13,350  lb.,  the  safe  working  tensile 
stress  of  the  material  being  15,000  lb.  per  sq.  in. 

Solution. — The  area  required  is  13,350  lb.  -p  15,0001b.  =  .890 
sq.  in.  at  the  root  of  the  thread ;  from  the  table,  it  will  bo 
found  that  a  rod  If  in.  in  diameter  will  suffice. 

In  designing  tension  bars  it  would  be  well  to  observe  the 
following :  Proportion  the  heads  of  eyebars  so  that  the  bar 
will  break  in  the  body  instead  of  in  the  eye ;  the  pin  hole 
should  be  ^  of  an  inch  larger  than  the  pin  ;  all  rivet  holes  in 
eyebars  should  be  drilled  and  the  wire  edge  cut  off;  bars 
should  be  thoroughly  annealed  after  forging,  and  no  smith- 
work  should  be  done  at  a  blue  heat ;  small  tension  rods  up  to, 
say,  If  in.  square  are  preferably,  either  simple  loop  or  clevis 
rods ;  the  eyes  of  loop  rods  should  be  bored  to  fit  the  pin 
upset  screw  ends  should  have  a  net  section  at  root  of  thread 
15  per  cent,  greater  than  the  body  of  the  bar ;  steel  rods  may 
be  used  for  upset  screw  ends,  but  should  be  tested  in  full  size 
section,  and  thoroughly  annealed  after  forging;  clevises, 
twinbuckles,  and  sleeve  nuts  should  be  of  standard  approved 
pattern. 


STRENGTH  OF  RIVETS  AND  PINS. 


139 


TABLE  XXXI. 

Bolts  and  Nuts. 


Bolts.  Nuts. 

U.  S.  Standard  Screw  Thread.  Manufacturers’  Standard. 


Biam.  of  Bolt.  In. 

No.  of  Threads 
per  Inch. 

Diam.  at  Root  of 
Thread.  Inches. 

Area  of  Bodv  ot 
Bolt.  Sq.  in. 

Area  at  Root  of 
Thread.  Sq.  In. 

Hexagon. 

Square. 

Short  Diam. 
Inches. 

Long  Diam. 

Inches. 

Side  of 

,  Square.  (In.) 

Diagonal. 

Inches. 

1 

4- 

20 

.185 

.049 

.027 

1 

.58 

1 

9 

.71 

6 

ts 

18 

.240 

.077 

.045 

* 

.72 

.88 

i 

8 

16 

.294 

.110 

.068 

* 

.87 

1 

1.06 

7 

is 

14 

.344 

.150 

.093 

7. 

1.01 

1.24 

i 

9 

13 

.400 

.196 

.126 

1 

1.15 

1 

1.41 

T93 

12 

.454 

.249 

.162 

1} 

1.30 

n 

1.59 

t 

11 

.507 

.307 

.201 

It 

1.44 

H 

1.77 

* 

10 

.620 

.442 

.302 

If 

1.59 

H 

2.12 

7 

8 

9 

.731 

.601 

.419 

If 

1.88 

if 

2.47 

1 

8 

.837 

.785 

.550 

11 

2.02 

2 

2.83 

H 

7 

.940 

.994 

.694 

2 

2.31 

2* 

3.18 

H 

7 

1.060 

1.230 

.890 

2£ 

2.60 

2i 

3.54 

if 

6 

1.160 

1.480 

1.060 

2i 

2.89 

2f 

3.89 

H 

6 

1.280 

1.770 

1.290 

2f 

3.18 

3 

4.24 

1* 

5g- 

1.390 

2.070 

1.510 

3 

3.46 

3i 

4.60 

if 

5 

1.490 

2.400 

1.740 

3£ 

3.75 

3| 

4.95 

H 

5 

1.610 

2.760 

2.050 

3* 

4.04 

3f 

5.30 

2 

41 

^9 

1.710 

3.140 

2.300 

3* 

4.04 

4 

5.66 

OJL 

•^4 

41 

^9 

1.960 

3.980 

3.020 

3# 

4.33 

4} 

6.01 

2i 

4 

2.170 

4.910 

3.710 

4i 

4.91 

4y 

6.36 

2$ 

4 

2.420 

5.940 

4.620 

4* 

5.20 

4f 

6.72 

3 

3^ 

2.630 

7.070 

5.430 

4$ 

5.48 

5 

7.07 

3i 

3* 

2.880 

8.300 

6.510 

5 

5.77 

51 

7.78 

3* 

3i 

3.100 

9.620 

7.550 

5i 

6.06 

5f 

8.13 

3 f 

3 

3.320 

11.040 

8.640 

6 

6.93 

6i 

9.19 

4 

3 

3.570 

12.570 

10.000 

65 

7.51 

7 

9.90 

41 

■*9 

21 

4.030 

15.900 

12.740 

u 

8.58 

8 

11.31 

The  thickness  of  rough  bolt  heads,  either  hexagonal  or 
square,  is  one-half  the  short  diameter  or  side  of  square 
respectively ;  for  rough  nuts,  it  is  equal  to  the  diameter  of 
the  bolt.  Finished  heads  and  nuts  have  a  thickness  equal  to 
the  diameter  of  bolt  less  ^  in. 


140 


STRUCTURAL  DESIGN. 


ROOF  TRUSSES. 


PRINCIPLES  OF  STRESSES. 

Paralle'ogram  of  Forces.— In  Fig.  34,  forces  a  b  of  50  lb.  and 
c  b  of  100  lb.  act  at  b  in  the  directions  shown.  To  find  their 

combined  action,  draw 
c  b ,  to  any  scale,  equal  to 
100  lb.,  and  a  b  equal  to  50 
lb.  Thus,  if  the  scale  is 
i  in.  to  10 lb.,  c  b  =  2£in., 
and  a  b  =  H  in.  Draw 
a  d  parallel  to  c  b,  and  c  d 
to  a  b,  intersecting  at  d ; 
then  d  b,  called  the  re¬ 
sultant,  gives  the  direc¬ 
tion,  and,  by  scaling,  the 
amount  of  their  com¬ 
bined  action,  145  lb.  The  figure  abed  forms  a  parallelogram 
of  forces. 

Triangle  of  Forces. — Assume  forces  c  a  of 
1,000  lb.,  and  a  b  of  800  lb.,  acting  at  a, 

Fig.  35.  Make  distance  c  a,  to  any  scale, 
equal  to  1,000  lb.,  and  a  b  equal  to  800 
lb.;  draw  resultant  c  b,  which,  by  scaling, 
is  found  to  be  1,550  lb  ;  it  is  opposed  to 
the  direction  in  which  forces  c  a  and  a  b 
act  around  the  triangle.  This  figure  cab 
forms  a  triangle  of  forces. 

Polygon  of  Forces.— The  preceding  diagrams  may  be  called 
polygons  of  forces,  but  the  term  is  usually  applied  to  diagrams 
determining  the  resultant  of  several  forces.  When  a  number 
of  forces  act  as  at  d,  Fig.  36,  their  resultant  is  obtained 
thus :  Draw  a  line  parallel  to  and  having  the  same  direction 
(as  indicated  by  the  arrow  points)  and  magnitude  as  one  of 
the  forces.  At  the  end  of  this  line,  draw  one  parallel  to 
a  second  force,  having  the  same  direction  and  magnitude  as 
this  second  force.  Continue  thus  until  all  the  forces  have 
been  plotted ;  a  straight  line  joining  the  free  ends  of  the 


ROOF  TRUSSES. 


141 


first  and  last  lines  will 
be  the  closing  side  of  the 
polygon ;  mark  it  oppo¬ 
site  in  direction  to  the 
other  forces,  of  which  it 
will  be  the  resultant. 

Thus,  the  resultant  of 
the  4  forces  acting  at  d 
is  obtained  by  drawing 
1-2,  2-3,  3-4,  4 -5,  parallel 
and  equal  to  forces  a  d, 
bd,  cd,  and  e  d,  respect¬ 
ively.  Connecting  5  and  1,  the  resultant  is  obtained. 


Resolution  of  Forces.— Since  the  effect  of  several  forces  may 
be  determined  by  a  single  resultant,  so  may  one  force  be 

resolved  into  several.  For  ex¬ 
ample,  the  force  ah,  Fig.  37,  may 
be  resolved  into  any  two  directions 
by  drawing  components  parallel  to 
those  directions.  Thus,  from  a 
draw  ac  vertically,  and  from  b 
draw  cb  horizontally,  intersecting 
at  c;  then  ac  is  the  vertical  component,  and  cb,  the  horizontal 
component  of  a  b. 

Frame  and  Stress  Diagrams. — In 
(a),  Fig.  38,  1,000  lb.  is  supported 
at  c  by  cords  ca  and  cb,  secured 
at  a  and  b.  This  figure,  drawn 


1000  lb. 
(a) 


a 


J 


Fig.  38. 


142 


STRUCTURAL  DESIGN 


to  scale,  accurately  represents  the  outline  of  the  structure,  and 
is  called  &  frame  diagram.  To  obtain  the  stresses  in  c  a  and  c  b, 
draw  1-2,  in  (&),  making  its  length  to  any  scale  and  direction 
represent  the  magnitude  and  action  of  W.  Thus,  if  1  in.  = 
400  lb.,  1-2  =  21  in.  long,  and,  its  direction  being  vertical  in 
(a),  it  is  so  drawn  in  (b).  From  1  draw  1-3  parallel  to  a  c,  and 
from  2  draw  2-3  parallel  to  c  b ;  they  intersect  at  3,  forming 
with  1-2  a  triangle.  If  1-3  and  2-3  are  measured,  using  same 
scale  as  for  1-2,  the  stresses  c  a  and  c  b  may  be  obtained.  Dia¬ 
gram  (6)  is  called  a  stress  diagram. 


STRESSES  IN  ROOF  TRUSSES. 

In  designing  roof  trusses,  two  stress  and  two  frame  dia¬ 
grams  are  generally  drawn,  one  of  each  for  the  dead  loads, 
which  act  vertically,  and  the  others  for  wind  loads,  usually 
taken  as  normal  to  the  slope. 

That  the  frame  and  stress  diagrams  may  be  conveniently 
compared,  the  following  system  of  lettering  may  be  employed : 
In  the  frame  diagram,  write  capital  letters  within  every  space 
that  is  cut  off  from  the  rest  of  the  figure  by  lines,  real  or 


imaginary,  along  which  forces  act,  as  in  Fig.  39.  Then  the 
member  is  named  from  the  letters  of  the  space  it  divides ; 
thus,  B  K  designates  the  lower  quarter  of  the  left-hand 
rafter ;  M  L,  the  first  vertical  tension  rod  from  the  left,  etc. 
The  stresses  in  these  members  are  designated  by  similar 
small  letters  in  the  stress  diagram  ;  thus,  the  stress  in  B  IT  is 
bk  in  Fig.  40,  and  in  M  L  is  vil.  It  is  to  be  understood  that 


ROOF  TRUSSES. 


143 


wherever  capital  letters  are  used,  reference  is  made  to  the 
frame  diagram ;  and  where  small  letters  are  used,  reference  is 
made  to  the  stress  diagram. 

Analysis  of  Howe  Roof  Truss. —  Vertical-Load  Diagrams—  To 
explain  the  above  principles  in  laying  out  stress  diagrams  for 
roof  trusses,  and  the  a 

determination  of  the 
amountandkindof  stress 
in  any  member,  the  ver¬ 
tical  and  wind-stress 
diagrams  will  be  drawn 
for  a  Howe  roof  truss, 

Fig.  89 ;  this  shows  the 
frame  diagram  with  the 
vertical  loads,  which  may 
be  figured  from  Table  I, 
page  62.  Since  the  loads 
are  equal  and  symmet¬ 
rically  placed,  each  reac¬ 
tion  will  be  one-half 
the  total  load.  Letter 
the  frame  diagram  as  shown,  and  proceed  with  the  stress 
diagram,  Fig.  40.  The  external  forces,  which  include 
loads  and  reactions,  having  been  determined  (this  should 


be  done  in  every  case),  draw  the  load  line  aj  vertically, 
as  that  is  the  direction  in  which  the  forces  act.  With  any  con¬ 
venient  scale,  make  ab,  be,  cd,  etc.  equal,  respectively,  to  the 
calculated  forces  AB,  B  C,  CD,  etc.  The  reactions  JZand  ZA, 
being  equal,  2  is  located  midway  between  j  and  a.  Then  the 
'polygon  of  external  forces,  as  it  is  called,  is  from  a  to  b,  b  to  c, 
c  to  d,  d  to  e,  and  so  on  to  j,  where  the  reactions  return  on 
the  load  line  from  j  to  z,  and  from  z  to  a,  the  starting  point. 
It  will  be  observed  from  this  that,  though  a  straight  line  hns 
been  drawn,  in  reality  a  many-sided  polygon  has  been  traced, 
each  external  force  constituting  a  side. 

The  internal  forces,  or  the  stresses  in  the  truss  members, 
may  now  be  determined,  as  follows :  Beginning  at  the  left- 
hand  joint  in  the  frame  diagram,  the  forces  are  B  K,  KZ,  ZA, 
and  A  B.  Care  must  be  taken,  in  reading  these  forces,  to  go 


144 


STRUCTURAL  RESIGN. 


around  each  joint  in  the  same  direction  in  which  the  exter¬ 
nal  forces  were  designated.  From  b  draw  b  k  parallel  to  B  K , 
and  from  z  draw  z  k  parallel  to  K  Z ;  their  intersection  is  at  k, 
and  the  polygon  of  forces  around  the  joint  is  from  a  to  b, 
b  to  k,  k  to  z,  and  z  to  a,  the  starting  point.  After  having 
designated  all  the  forces  at  a  joint  in  the  stress  diagram, 
always  read  around  the  polygon  of  forces  as  given  above,  and 
see  that  it  closes,  that  is,  that  the  last  line  joins  the  first, 
forming  a  closed  figure.  Also,  note  the  direction  in  which 
the  forces  travel  along  each  line  in  the  stress  diagram,  and 
mark  the  same  by  arrowheads  upon  the  members  in  the  frame 
diagram.  Arrowheads  acting  away  from  a  joint,  as  in  K Z, 
denote  tension ;  those  acting  towards  one,  as  in  B  K,  denote 
compression. 

The  next  joint  is  B  CL K,  and  the  lines  determining  the 
stresses  are  obtained  by  drawing,  from  c,  cl  parallel  to  CL, 
and,  from  k,  l  k  parallel  to  LK;  their  intersection  is  at  l,  and 
the  polygon  of  forces  around  this  joint  is  from  c  to  l,  l  to  k, 
k  to  b,  and  b  to  c,  the  starting  point.  In  similar  manner  the 
stresses  around  any  joint  may  be  obtained. 

When  the  apex  joint  is  reached,  the  diagram  begins  to 
repeat;  thus, /g  is  the  same  as  ep.  It  is  therefore  unneces¬ 


sary  to  proceed  further,  as  the  loads  being  symmetrically 
placed,  the  stresses  in  the  right  half  of  the  truss  will  be 
identical  with  those  on  the  left  half. 


Wind-Load  Diagrams. — To  determine  the  wind  stresses,  the 


ROOF  TRUSSES. 


145 


frame  diagram  should  be  redrawn.  The  wind  loads,  con¬ 
sidered  as  acting  at  each  panel  point ,  may  be  determined 
from  Table  VII,  page  68,  and  are  shown  in  Fig.  41.  As  the 
ends  of  the  truss  are  secured  against  sliding,  the  reactions 
act  parallel  to  the  wind  pressures.  If,  however,  the  left  end 
of  the  truss  is  secured,  and  the  right  end  rests  on  rollers  (as 
is  sometimes  the  case  with  iron  or  steel  trusses  to  permit 
expansion),  the  right  reaction,  instead  of  being  parallel  to  the 
direction  of  the  wind,  would  be  vertical.  The  wind-stress 
diagram  for  such  a  truss  would,  with  this  exception,  be  found 
similarly  to  that  for  a  fixed-end  truss. 

To  determine  reactions  Ri  and  R2,  let  Rx  be  the  center 
of  moments ;  then  the  perpendicular  distance  between  the 
line  of  action  of  R2  and  the  point  Ri  is  71.22  ft.,  obtained 
by  extending  the  left-hand  rafter  to  intersect  the  line  of 
action  of  R»  at  y'.  Regard  Ay'  as  a  beam,  and  calculate 
reactions  R \  and  Ro  by  the  method  given  for  beams.  Taking 
moments  about  R\,  the  reaction  R2  is  found  to  be  3,516  lb.; 
and  Ri  =  11,200  lb.,  the  total  load,  —3,516  lb.  =  7,684  lb. 

Proceed  with  the 
wind-stress  dia¬ 
gram,  Fig.  42,  by 
drawing  the  load 
line  af  parallel  to 
the  direction  of  the 
wind  in  the  frame 
diagram.  Lay  off 
to  any  scale  the  for¬ 
ces  ab,bc,  cd,  etc., 
equal  to  4i?,  B  C, 

CD,  etc.,  respect¬ 
ively.  Then,  from 
a  lay  off  az,  equal 
to  reaction  Z  A,  or  Rx .  If  the  loads  have  been  laid  off  aceu. 

rately,  / z  should  be  equal  to  R*. 

The  first  joint  to  analyze  is  A  B  K Z.  Draw  b  k  parallel  to 
B  K ;  and  from  z,  zk  parallel  to  K Z ;  they  intersect  at  k.  The 
polygon  of  forces  is  from  a  to  b,  b  to  k,  k  to  z,  and  z  to  the  start¬ 
ing  point  a.  Joint  B  CL  K  is  analyzed  similarly. 


146 


STRUCTURAL  DESIGN. 


To  analyze  joint  KLMZ:  kl  being  known,  the  next  mem¬ 
ber  is  L  M ;  from  l  draw  Im,  parallel  to  LM.  As  the  next 
member  is  M Z,  to  which  m  z  is  parallel,  the  point  m  is  located 
where  Im  intersects  mz ;  this  completes  this  joint,  the  poly¬ 
gon  of  forces  being  ftom  k  to  l,  l  to  m,  m  to  z,  and  sto  k.  The 
stresses  at  the  other  joints  may  be  found  in  the  same  way  as 
those  explained.  The  members  shown  in  dotted  lines  do  not 
sustain  wind  stresses  when  the  wind  blows  upon  the  left  side 
of  the  truss. 

The  final  joint  is  EFQP,  at  which  there  is  only  one 
unknown  force — the  stress  in  FQ.  A  line  drawn  from  / 
parallel  to  F  Q  should  pass  through  q.  This  is  always  a  test 
of  the  accuracy  of  the  work,  and  if  the  last  line  does  not 
close  on  the  proper  point,  when  drawn  parallel  to  the  mem¬ 
ber  it  represents,  the  stress  diagram  should  be  redrawn,  to 
determine  whether  the  loads  and  reactions  have  been  laid 
out  correctly,  and  whether  any  joint  or  member  has  been 
omitted. 

The  two  diagrams  completed,  scale,  in  round  numbers, 
the  stresses  in  each  member,  indicating  compressive  and  ten¬ 
sile  stresses  by  plus  and  minus  signs,  respectively.  Tabulate 
results  as  follows : 


Member. 

Vertical  Load. 
Pounds. 

Wind  Load. 
Pounds. 

Total. 

Pounds. 

BK 

+  27,000 

+  12,000 

+  39,000 

CL 

+  23,500 

+  10,000 

+  33,500 

DN 

+  19,500 

+  7,600 

+  27,100 

EP 

+  16,000 

+  5,680 

+  21,680 

KZ 

—  24,000 

—  13,300 

—  37.300 

MZ 

-  21,000 

—  it),  000 

—  31,000 

OZ 

-  17,500 

—  7,000 

—  24,500 

LK 

+  4,000 

+  3,500 

+  7,500 

NM 

+  5,000 

-f  4,400 

+  9,400 

PO 

+  6,500 

+  5,400 

•+  11,900 

ML 

—  1,600 

1,500 

—  3,100 

ON 

—  3,500 

-  3,000 

—  6,500 

QP 

—  10,600 

4,500 

—  15,100 

FQ 

+  16,000 

f  6,600 

+  22,600 

ROOF  TRUSSES. 


147 


Analysis  of  Stresses  in  a  Fink  Roof  Truss. — This  truss,  shown 
in  Fig.  43,  is  much  used  for  pin-connected  and  structural-steel 
trusses. 


Vertical-Load  Diagrams. — Obtain  the  forces  acting  at  each 
panel  point  and  draw  the  frame  diagram  for  the  vertical 
loads,  as  in  Fig.  43.  Since  the  loading  is  symmetrical,  the 
reactions  Rx  and  R2  will  each  he  one-half  the  load,  or  27,200  lb. 
Draw  in  the  stress  diagram,  Fig.  44,  the  load  line  abode,  etc., 
locating  z  midway  between  e  and/.  The  polygon  of  external 
forces  will  be  from  a  to  b,  b  to  c,  c  to  d,  etc.,  until  j  is  reached ; 
retracing  the  load  line 
from  j  to  z  gives  R-> ,  and 
from  z  to  a  determines  Rx. 

Analyzing  each  joint 
as  before  shown,  no  diffi¬ 
culty  will  be  met  until  the 
joints  CD  ON  ML  and 
MNQZ are  reached ;  it  is 
found  that  three  un¬ 
known  forces  exist  at 
each  of  these  joints,  and, 
as  it  is  impracticable  to 
determine  the  stresses 
graphically  when  more  than  two  forces  are  unknown,  the 
value  of  one  must  be  otherwise  obtained.  Upon  inspecting 
the  frame  diagram,  it  will  be  observed  that  the  joint  at  B  C  is 


148 


STRUCTURAL  DESIGN. 


similar  to  D  E ;  and  it  is  reasonable  to  suppose  that  L  K  will 
have  an  equal  stress  with  P  0.  From  this  it  would  appear  that 
there  must  be  an  equal  and  like  stress  exerted  by  L  M,  to  retain 
the  foot  of  L  K  in  position,  as  is  exerted  by  0  N  to  keep  P  0  in 
place.  The  stresses  in  M L  and  L  C  being  known,  that  in  D  0 
may  be  determined  by  drawing  a  line  from  d  parallel  to  D  0,  to 
such  a  point  o  that— having  drawn  on  equal  in  length  to  Im 
—the  line  nm,  parallel  to  NM,  will  close  on  to.  The  polygon 
of  forces  will  be  from  to  to  l,  l  to  c,  c  to  d,  dtoo,o  to  n,  and 
n  to  to,  the  starting  point. 

The  joint  MNQZ  now  offers  no  difficulty  to  solution, 
as  mn  has  been  previously  determined.  The  final  joint 
OP  QN may  be  solved  by  drawing  from p  a  line  parallel  to 
P  Q,  which  will,  if  the  diagrams  have  been  correctly  drawn, 
pass  through  n,  and  from  this  point  will  coincide  with  n  q. 

One  half  the  vertical-load  diagram  being  completed,  and 
the  loading  being  symmetrical,  it  is  unnecessary  to  draw  the 


other  half  unless  as  a  check.  The  equality  of  the  triangles 
l  k  to  and  pon,  and  their  resemblance  to  nmq,  greatly  assist 
in  drawing  diagrams  for  trusses  of  this  type. 

Method  of  Trial  for  Obtaining  Third  Unknown— It  one 
unknown  stress  prevents  the  solution  of  the  diagram,  it  may 
sometimes  be  found  by  trial.  Thus,  assume  the  amount  of 
unknown  stress  and  proceed  with  diagram  ;  if  it  fails  to  close, 
again  assume  amount  of  unknown  stress  and  try.  Proceed 
thus  until  diagram  closes. 


ROOF  TR  USSES. 


149 


Wind-Stress  Diagrams. — First  find  the  external  forces  and 
reactions,  as  in  the  Howe  truss,  page  143,  and  redraw  the  frame 
diagram,  as  in  Fig.  45. 

The  solution  of  the 
wind-stress  diagram, 

Fig.  46,  offers  the  same 
difficulties  as  in  draw¬ 
ing  the  vertical-load 
diagram,  and  may  be  ^ 
similarly  solved.  The 
last  joint  FR  QPE  is 
solved  by  drawing  from 
/  a  line  parallel  to  FR, 
and  from  q,  a  line  par¬ 
allel  to  R  Q ;  their  inter¬ 
section  is  at  r,  and  the  polygon  of  forces  is  from  e  to  f,J 
to  r,  r  to  q,  q  to  p,  and  p  to  e. 


DETAIL  DESIGN  OF  ROOF  TRUSSES. 

Trusses  subjected  to  wind,  acting  perpendicular  to  the  gable, 
should  be  braced  with  diagonal  braces  connecting  the  several 
trusses.  If,  however,  the  roof  sheathing  is  of  planking  secured 
directly  to  the  trusses,  and  especially  if  run  diagonally,  other 
bracing  may  not  be  required.  If  stone  gables  protect  the 
roof  in  a  longitudinal  direction,  lateral  bracing  may  in 
many  cases  be  omitted. 

The  vertical  and  wind  loads  of  a  truss  may  be  figured  from 
Tables  I,  VII,  pages  62,  68.  The  weight  of  the  truss  is  the 
most  uncertain  factor,  being  practically  unascertainable 
until  the  design  is  made  ;  hence,  it  is  well,  after  designing 
the  truss,  to  calculate  and  compare  its  weight  with  that 
assumed. 

The  stresses  being  determined,  the  members  must  be 
proportioned  to  sustain  them.  Roof  trusses  differ  from 
bridge  trusses  in  that  the  loads  are  generally  statical  and 
not  suddenly  applied  ;  consequently,  a  smaller  factor  of 
safety  may  be  employed.  It  is  the  practice,  in  ordinary 
construction,  to  employ  for  timber  members  in  a  roof  truss  a 


150 


STRUCTURAL  DESIGN. 


factor  of  safety  of  from  4  to  6  ;  and  for  structural  steel  and 
wrought  iron,  3  to  4  ;  cast  iron  is  seldom  used  in  roof  trusses, 
and  is  never  used  with  a  factor  of  safety  less  than  10,  unless 
the  load  creates  compressive  stress  only,  in  which  case  a 
somewhat  smaller  factor  may  be  used.  The  factor  of  safety 


r-2'py--24',-~ 
H* - *--[  o - 

—24^—?4^\ 

i  ;i  . . J— {j — H 
-ri!  li  ■ — ti — if— 1 

T-jir — e - & - ®v- 

— r* 

:!  U  !:  r-4- — t-, 

■7^ - w  io - 

Detaihf  Splice  in  Tie  Mem  bet 
Coffers 


Wrt Iron  Washer /"ThicK.  - 
Purlins.^ 

ifdiaPod^ 


i "  <  v->  --  - ,  l  •>  j, 

detail  of  Joints  on  Tie  Member  Sphce plate  not shotv/i. 
,»  Yellow fine /A  t2-fPa it  Dowel 

/i'Rnir  <-A\  \  Mns  aboutik" 
/aw$L  JMjecfio/iin 

Sj  \  ^^Casr Ironiuo^fyT^fl^  '  'yr 


fairs  Yeiiotvfine/ 

^  Cori  t  Purhn4m 
m  (Lagjcrews  /r 


iv/ 

^  IH?  \mjnj/e 

'’''•I  <§t|\  Fig.  47. 


{Strut 


is  much  a  matter  of  judgment,  and  may  be  altered  as  the 
designer’s  experience  dictates. 

Tension  members  are  liable  to  fail  at  the  least  cross- 
section  ;  therefore,  the  screw  ends  of  long  rods  and  bolts 
should  be  enlarged,  so  that  the  cross-section  at  the  root  of 
the  threads  will  be  at  least  as  large  as  elsewhere.  Allowance 


ROOF  TRUSSES. 


151 


'dOfTfsmC&freTvCetirreofMbordoto — 


152 


STRUCTURAL  DESIGN. 


ROOF  TRUSSES.  153 


154 


STRUCTURAL  DESIGN. 


must  be  made  for  diminution  of  cross-section  by  bolt  or  rivet 
holes.  To  determine  the  net  section  required  in  any  tension 
member,  divide  the  stress  upon  the  member  by  the  allowable 
tensile  stress  of  the  material. 

In  proportioning  compression  members,  the  length  of 
which  is  not  over  from  8  to  10  times  the  diameter  or  least 
side,  the  cross-section  may  be  figured  by  dividing  the  stress 
by  the  allowable  direct  unit  compressive  stress.  If,  however, 
the  length  exceeds  these  dimensions,  the  members  must  be 
regarded  as  columns,  and  figured  as  such.  If  a  member  is 
subjected  alternately  to  compression  and  tension,  its  section 
should  be  somewhat  increased  over  that  required  to  sustain 
either  stress. 

Where  the  rafter  members  of  a  truss  support  purlins 
between  the  panel  points,  the  members  are  subjected  to 
bending,  as  well  as  to  direct  compressive  stress.  In  design¬ 
ing  them,  it  is  customary,  with  wooden  members,  to  propor¬ 
tion  them  by  first  determining  the  proper  size  of  beams  to 
sustain  the  transverse  stress,  and  adding  sufficient  sectional 
area,  by  increasing  the  width,  to  sustain  the  direct  compres¬ 
sive  or  tensile  stress,  as  the  case  may  be.  Where  the  direct 
stress  is  compressive,  it  should  be  also  checked  by  applying 
the  column  formulas.  Structural-steel  or  wrought-iron  mem¬ 
bers  are  usually  proportioned  for  the  bending  stress,  the  direct 
stresses  being  provided  for  by  increasing  the  thickness  of  the 
rolled  section,  care  being  taken  that  the  sum  of  the  extreme 
transverse-fiber  stress  and  direct-fiber  stress  is  not  more  than 
the  safe  stress  of  the  material. 

Where  members  are  connected  by  bolts  or  pins,  the  pins 
are  usually  prox>ortioned  to  sustain  the  transverse  stresses, 
and,  if  so  proportioned,  generally  have  sufficient  resistance  to 
shearing.  Strength  of  pins  is  treated  on  pages  133-187, 
and  the  information  given  there  will  be  found  sufficient. 
Since  the  direct  stresses  in  members  connected  at  a  common 
joint  by  a  pin  creates  bending  stresses  upon  the  pin,  the 
members  should  be  packed  closely,  and  those  members  hav¬ 
ing  opposite  stresses  brought  in  juxtaposition  if  possible. 

In  designing  any  structure,  and  especially  roof  trusses,  the 
following  points  should  be  carefully  observed:  (a)  Propor- 


ARCHES. 


155 


tion  all  parts  of  a  joint  so  that  the  maximum  strength  will  he 
realized  throughout,  in  order  that  one  part  will  not  he  likely  to 
yield  before  another.  ( b )  Weaken  as  little  as  possible  the  pieces 
connected  at  a  splice,  (c)  Give  sufficient  hearing  surface 
to  bring  the  compression  on  the  surface  well  within  the  safe 
limits,  so  that  there  will  be  no  danger  of  crippling  plates  or 
crushing  the  ends  of  members  before  their  maximum  strength 
is  realized.  ( d )  Distribute  rivets  and  holts  so  as  to  give  the 
greatest  resistance  with  the  least  cutting  away  of  other  parts. 
( e )  See  that  the  central  axis  of  every  member  coincides  as 
nearly  as  possible  with  the  line  of  action  of  the  stress. 
(/)  Examine  all  sections  and  parts  for  tensile,  compressive, 
transverse,  and  shearing  stresses.  ( g )  Finally,  hear  con¬ 
stantly  in  mind  that  the  strength  of  a  structure  depends 
on  the  strength  of  its  weakest  part,  and  that  the  failure  of 
a  single  joint  may  he  as  fatal  to  the  life  of  a  structure  as 
though  a  member  were  insufficient. 

A  close  study  of  the  details  of  the  trusses  shown  in  Figs. 
47,  48  and  49,  in  connection  with  the  foregoing  explanations 
of  principles,  will  give  a  general  idea  of  how  such  parts  are 
designed.  _ 


Principles.— Let 

resultants  of  all 
the  loads  on  the 
left  and  right 
halvesof  thearch, 
respectively,  and 
let  Pi  he  equal  to 
P2,  and  located 
equally  distant 
from  the  crown. 

Let  Pi  and  P2  rep¬ 
resent  the  verti¬ 
cal  reactions, 
which,  since  the 
loads  are  sym¬ 
metrically  placed,  are  equal 


ARCHES. 

and  P2,  in  Fit 


50  (a),  represent  the 


Fig.  50. 

Let  b  be  the  horizontal  distance 


156 


STRUCTURAL  DESIGN. 


between  Rx  and  Pi ;  also  between  P2  and  P2,  or,  in  other 
words,  the  leverage  of  Px  and  P2  with  respect  to  Px  and  P2. 
Let  Q  be  the  horizontal  thrust,  which  is  equal  at  all  points ; 
also,  let  c  be  the  leverage  of  Q  with  respect  to  the  crown.  Now 
assume  the  right-hand  half  of  the  arch  to  be  taken  away,  as 
in  (5).  To  preserve  equilibrium  in  the  left  side,  the  force  Qi 
must  be  supplied  at  the  crown.  The  algebraic  sum  of  the 
vertical  forces,  and,  likewise,  the  sum  of  the  horizontal  forces, 
must  equal  zero,  or  there  will  not  be  equilibrium.  Then  R} 
must  equal  Pi,  and  Qi  must  equal  Q.  Also,  the  sum  of  the 
moments  about  any  point  must  equal  zero.  Hence,  taking 
moments  about  the  abutments  in  (a),  Qc  =  Pi  b,  and 
P  b 

Q  =  ;  also,  since  the  arch  is  symmetrically  loaded, 


„  P2  b  ,  Pi  b  P2  b 
QoC  =  — —  and 


In  this  case  Pi  or  P2  may 


c  c  c 

represent  any  number  of  loads,  provided  they  are  equal 
and  symmetrically  placed. 


METHODS  OF  DETERMINING  THE  LINE  OF 
PRESSURE. 

Line  of  Pressure.— If  a  cord,  fastened  at  each  end,  supports 
a  number  of  loads,  it  will  take  a  position  of  equilibrium, 

depending  on  the 
amount  and  loca¬ 
tion  of  the  loads, 
as  in  (o),  Fig.  51. 
In  such  a  case,  the 
cord  is  in  tension. 
If  the  system  is 
inverted,  it  will 
assume  the  posi¬ 
tion  shown  in  (b), 
in  which  the 
forces  are  still  in 
equilibrium;  but, 
Instead  of  a  cord  in  tension,  the  lines  op,pq ,  etc.  must  be 
members  capable  of  resisting  compression.  This  latter  case 


ARCHES. 


157 


represents  what  exists  in  an  arch,  and  the  broken  line  inter¬ 
secting  the  vertical  forces  forms  the  line  of  pressure;  the 
material  in  the  arch  must  be  of  such  strength  and  so  disposed 
as  to  safely  resist  the  compressive  forces  acting  along  this 
line. 

To  determine  the  line  of  pressure  for  any  arch,  points  at 
the  abutments  and  crown  must  be  fixed  upon  ;  otherwise,  an 
indefinite  number  of  lines  of  pressure  could  be  drawn.  In 
metal  arches,  the  abutments  and  crown  are  generally  hinged, 
or  pin-connected,  and  the  line  of  pressure  necessarily  passes 
through  these  three  points.  In  masonry  arches  the  abutments 
and  crown  are  generally  not  hinged,  although  there  are 
exceptions ;  and,  therefore,  a  point  must  be  assumed  at  each 
abutment  and  at  the  crown,  through  which  the  line  of  pres¬ 
sure  is  to  pass.  The  line  of  pressure  should,  for  a  masonry 
arch,  be  within  the  middle  third  of  the  arch  ring,  the  depth 
of  keystone  of  which  is  first  assumed,  or  made  equal  to  that 
of  some  existing  arch  of  about  the  same  span.  Thus,  with  an 
arch  3  ft.  deep,  the  line  of  pressure  should  be  within  a  space 
6  in.  on  either  side  of  the  center  of  the  depth.  If  it  lies  with¬ 
out  the  middle  third,  the  joints  tend  to  open,  which  result, 
while  the  danger  of  failure  of  the  arch  may  not  be  great, 
would  be  unsightly.  Again,  if  the  line  of  pressure  passes 
through  the  middle  third,  the  angle  that  it  makes  with  any 
joint  will  not  be  such  that  the  voussoirs  are  likely  to  slide  on 
their  surface  of  contact. 

In  taking  the  loads  upon  arches,  all  weights  must  be 
reduced  to  the  same  standard  ;  that  is,  in  this  case,  the 
loads  have  been  made  equivalent  to  masonry  weighing 
140  lb.  per  cu.  ft.  The  arch  and  loads  are  assumed  to  be  1  ft. 
in  thickness,  so  that  all  superficial  measurements  also  repre¬ 
sent  cubic  contents. 

Analytic  Method.— In  the  arch  shown  in  Fig.  52  (a),  the  pres¬ 
sure  curve  is  considered  as  passing  through  points  at  the 
abutments  f  the  depth  of  the  voussoirs  from  the  intrados, 
and  through  the  center  of  depth  at  the  crown.  The  theoreti¬ 
cal  rise  of  the  arch  is  10.75  ft.,  and  the  theoretical  span, 
51.32  ft.  The  arch  and  load  is  divided  by  dotted  lines  into 
sections,  which,  for  convenience,  are  numbered. 


158 


STRUCTURAL  DESIGN. 


If  w  be  the  width  of  any  section,  and  h  its  height,  then 
its  area  a  is  w  X  h.  Also,  if  c  is  the  distance  from  the  crown 
to  the  center  of  gravity  of  a  section,  the  moment  m  of  any 
section  about  the  crown  is  a  X  c.  Call  A  the  sum  of  all 
the  a’s  from  the  crown  up  to  and  including  the  section 


considered ;  thus,  A  for  section  3  is,  in  the  following  table, 
31.25  +  63.75  +  70.  Call  M  the  total  of  the  m’s ;  thus,  M  for 
section  3  is  78.12  +  478.12  +  875.  Then,  the  distance  C  from 
the  crown  to  the  center  of  gravity  of  the  portion  between 


ARCHES. 


159 


the  crown  and  the  section  considered  is  —  of  that  section 

A 

(see  Neutral  Axis,  page  75)  ;  thus,  for  section  3,  the  distance  C 

1  431  24 

for  the  portion  including  the  sections  1,  2,  and  3  is  ■  *  ' — 


=  8.67  ft. 

The  above  .values  may  be  tabulated  as  follows : 


Section. 

w 

h 

a  = 
w  X  h 

c 

m  = 
a  X  c 

A  = 

2  a 

M  = 

2  m 

C  = 

M 

A 

1 

5 

6.25 

31.25 

2.5 

78.12 

31.25 

78.12 

2.50 

2 

5 

12.75 

63.75 

7.5 

478.12 

95.00 

556.24 

5.85 

3 

5 

14.00 

70.00 

12.5 

875.00 

165.00 

1,431.24 

8.67 

4 

5 

16.50 

82.50 

17.5 

1,443.75 

247.50 

2,874.99 

11.61 

5 

5 

14.00 

70.00 

22.5 

1,575.00 

317.50 

4,449.99 

14.01 

6 

2 

14.75 

29.50 

26.0 

767.00 

347.00 

5,216.99 

15.03 

cc  X  -P 

The  horizontal  thrust,  Q  —  — ^ — ,  in  which  x  is  equal  to 

one-half  the  theoretical  span,  or  25.66  ft.  minus  the  value 
of  C  for  the  6th  section,  which  is,  in  this  case,  15.03,  giv¬ 
ing  x  —  10.63 ;  P  is  equal  to  A  for  the  last  section,  347 ;  and 
b  equals  the  theoretical  rise  of  the  arch,  10.75  ft.  Hence, 
.  i  .  ,  .  ,  -  x  X  P  10.63  X  347 

b  10.75 

cu.  ft.  Multiplying  by  140  lb.,  the  weight  of  masonry  per 
cubic  foot  assumed  in  this  case,  the  horizontal  thrust  is 
48,020  lb. 

The  line  of  pressure  may  now  be  determined  as  follows: 
Draw  through  point  p  in  Fig.  52  (5),  the  horizontal  line  yz; 
lay  off  to  scale  from  p,  in  order,  the  distances  C  obtained  from 
table.  At  these  points  lay  off  the  vertical  distance  ef,  g  h',  ij, 
etc.,  equal  respectively  to  the  values  31.25,  95, 165,  etc.,  from 
the  column  headed  A.  For  instance,  if  the  diagram  is  drawn 
to  a  scale  of  1  in.  to  100  cu.  ft.,  the  distance  ef  will  be  .31,  or 
nearly  j  in.  From  f  h',  j,  etc.,  to  the  same  scale,  mark  off  the 
constant  horizontal  thrust  Q,  as  at  f  q,  h'  r,  j  s,  etc.  Thus, 


i 


160 


STRUCTURAL  DESIGN . 


the  vertical  and  horizontal  forces  at  each  section  being  given, 
the  resultant  of  these  two  forces  in  each  case  is  eq,g  r,  i  s,  etc. 
Extending  each  until  it  intersects  the  joint  beyond  e,  g,  i,  etc., 
the  pressure  curve  may  be  drawn  through  these  latter 
points  of  intersection,  as  shown  by  the  heavy  black  line, 
and  the  thrust  at  the  joints  may  be  found  by  measuring  e  q, 
gr,  is,  etc.  with  the  scale  to  which  the  diagram  was  drawn. 

Since  in  this  case  the  pressure  curve  falls  well  within  the 
middle  third  of  the  arch  ring,  the  arch  may  be  consid¬ 
ered  satisfactory,  provided  the  safe  crushing  strength  of  the 
masonry  is  not  exceeded. 

The  influence  of  the  last  oblique  thrust,  which  is  the 
resultant  thrust  of  the  arch  upon  the  pier,  or  abutment,  will 
be  explained  in  the  following  method  of  determining  the 
pressure  curve.  This  method  is  somewhat  simpler,  as  it 
requires  practically  no  calculations. 


Graphic  Method. — Fig.  53  shows  the  wholly  graphic  method 
of  finding  the  line  of  pressure.  It  is  for  a  6-rowlock  brick 
segmental  arch,  24  ft.  span,  2  ft.  10  in.  rise,  and  26  ft.  radius 
of  intrados. 


ARCHES. 


161 


Begin  by  drawing,  to  scale,  a  diagram  of  one-half  the  arch. 
As  in  the  previous  example,  the  arch  and  its  load  is  con¬ 
sidered  to  be  1  ft.  thick ;  and  the  brickwork  weighs  140  lb. 
per  cu.  ft.  A  load  of  9,200  lb.  upon  one-half  the  arch  has 
been  assumed.  Lay  off,  to  scale,  a  height  of  brickwork 
whose  weight  will  represent  this  load.  Commencing  at  the 
crown,  divide  the  load  into,  say,  sections  of  2  ft.,  as  far  as 
possible.  The  weight  of  each  slice  will  be  its  contents  mul¬ 
tiplied  by  140  lb.,  and  is  marked  on  the  diagram.  Next,  fix  a 
point  at  the  crown,  and  one  at  the  spring  of  the  arch,  through 
which  the  pressure  curve  is  assumed  to  pass.  The  points 
may  lie  anywhere  within  the  middle  third  of  the  width ; 
but  the  point  a  at  the  crown  has  been  taken  at  the  outer 
edge,  and  the  point  u  at  the  spring  at  the  inner  edge,  of  the 
middle  third.  Lay  off  from  a,  on  the  vertical  a  d' ,  the  dis¬ 
tances  ab,bc,cd,  etc.,  which  represent  the  weight  of  the 
slices  from  the  crown  to  the  spring.  Thus,  if  the  scale  were 
1  in.  per  1,000  lb.,  a  b  would  be  1.1  in.  long.  Next,  draw  45° 
lines  from  a  and  h,  intersecting  at  i ;  and  from  i  draw  i  b,  i  c, 
i  d,  etc.  Through  the  center  of  gravity  of  each  slice,  draw  a 
vertical,  as  o  v,  p  w,  q  x,  etc.  Starting  from  a,  draw  a  v  parallel 
to  ai ;  from  v,  draw  vw  parallel  to  bi,  etc.  These  lines  form 
a  broken  line,  which  changes  its  direction  on  the  vertical 
line  through  the  center  of  gravity  of  each  slice.  From  the 
last  point  k,  draw  kj  parallel  to  ih,  and  intersecting  ai, 
extended,  at  j ;  from,/  draw  a  vertical  line./Z,  which  will  pass 
through  the  center  of  gravity  of  the  half  arch  and  load. 
From  l,  where  the  horizontal  line  al  intersects  O',  layoff  a 
distance  Im  equal  to  ah ,  which  represents  the  weight  of  all 
the  slices.  From  l  draw  a  line  through  the  point  u  ;  and  from 
m,  a  horizontal  line  intersecting  l  u,  extended,  at  n.  Then 
m  n  will  be  the  horizontal  thrust  at  the  crown,  required  to 
maintain  the  half  arch  in  equilibrium  when  the  other  half  is 
removed ;  and  l  n  will  be  the  direction  and  amount  of  the 
oblique  thrust  at  the  skewback.  On  l  a  extc  ided,  lay  off, 
from  a,  a  distance  ab'  equal  to  mn.  From  b',  draw  lines  to 
b,  c,  d,  etc.,  which  represent  the  thrusts  at  the  center  of  gravity 
of  each  slice.  From  a,  draw  a  o,  parallel  to  b'  a  ;  from  o,  draw 
op,  parallel  to  b ’  b,  etc.;  then  a,  o,  p,  etc.  will  be  points  on  the 


162 


MASONRY. 


line  of  pressure.  If  this  line  lies  within  the  middle  third,  the 
arch  will  he  stable,  provided  the  pressure  is  within  safe 
limits.  The  pressure  at  u  is  found  by  measuring  b'  h  with  the 
same  scale  as  for  a  b,  be,  etc.,  and  is  about  16,000  lb.  Hard- 
burned  brick,  laid  in  cement  mortar,  will  safely  sustain  a 
compressive  stress  of  from  150  to  200  lb.  per  sq.  in.  The  area 
at  the  skewback,  144  sq.  in.,  multiplied  by  200,  gives  28,800  lb., 
which  is  well  within  the  safe  limit. 

The  stability  of  the  abutments  may  be  determined  thus : 
Having  calculated  the  weight  of  the  pier  or  wall,  lay  off  this 
weight  on  the  vertical  line  from  h  to  d' ,  and  draw  d'  b' .  Draw 
a  vertical  line  through  the  center  of  gravity  of  the  pier,  cutting 
In  at  c' ;  also,  a  line  from  c',  parallel  to  b' d'.  The  latter  line 
will  be  the  resultant  thrust  of  the  arch,  after  being  influenced 
by  the  weight  of  the  pier.  If  this  line  falls  beyond  the  foot 
of  the  pier,  at  the  ground  line,  the  pier  will  be  incapable  of 
resisting  the  thrust  of  the  arch.  In  order  that  a  pier  may  be 
secure,  this  final  or  resultant  line  of  thrust  should  fall  on  the 
ground  line,  well  within  the  middle  third  of  the  base. 


MASONRY. 


MATERIALS  OF  CONSTRUCTION. 


STO  N  E. 

Granite  is  the  most  valuable  stone  where  strength  is 
required,  its  crushing  strength  averaging  about  20,000  lb.  per 
sq.  in.  Owing  to  its  hardness,  it  is  very  costly  to  dress,  and 
its  use  is  limited  to  the  most  expensive  kinds  of  buildings. 
Granite  being  very  dense  and  compact,  absorbs  but  little 
water,  and  hence  is  valuable  in  damp  situations.  Exposed  to 
fire,  it  disintegrates  at  a  temperature  of  from  900°  to  1,000°  F., 
being  less  durable  in  this  respect  than  fine-grained  compact 
sandstones.  The  average  weight  of  granite  is  about  167  lb. 
per  cu.  ft. 

Limestone  is  a  very  common  building  stone,  and,  when 
compact,  is  very  durable.  It  is  usually  quite  absorptive,  and 


MATERIALS  OF  CONSTRUCTION. 


163 


becomes  dirty  quickly ;  while  under  intense  heat,  it  is  con¬ 
verted  into  lime.  Limestone  must  be  well  seasoned  before 
use,  to  get  rid  of  the  quarry  water.  The  strength  of  lime¬ 
stone  varies  from  7,000  to  25,000  lb.  per  sq.  in.,  the  average 
being  about  15,000  lb.  The  weight  of  limestone  is  about  155 
to  160  lb.  per  cu.  ft. 

Sandstone  is,  in  general,  an  excellent  building  stone, 
capable  of  resisting  great  heat,  and  the  better  kinds  absorb 
only  small  quantities  of  water.  The  dark-brown,  flinty  sand¬ 
stones  retain  their  color  very  well,  ranking  better  than 
granite.  A  stone  containing  much  pyrites  becomes  unevenly 
discolored,  due  to  formation  of  rust,  and  hence  the  stone 
should  be  carefully  examined  in  this  respect.  The  average 
strength  of  sandstones  is  about  11,0001b.  per  sq.  in.,  varying 
from  4,000  to  17,000  lb.  The  weight  of  sandstone  is  about  140 
lb.  per  cu.  ft. 

The  densest  and  strongest  stones  are  generally  the  most 
durable.  A  fresh  fracture,  when  examined  under  a  magni¬ 
fying  glass,  should  be  clear  and  bright,  showing  well- 
cemented  particles.  When  a  good  stone  is  tapped  with  a 
hammer,  it  gives  out  a  ringing  sound.  The  absorptive  quality 
of  a  stone  may  be  tested  by  noting  the  increase  in  weight 
after  soaking  in  water  for  24  hours.  One  that  increases  5  per 
cent,  or  more  should  not  be  used.  For  ordinary  building 
purposes,  tests  of  crushing  strength  are  unnecessary,  as  if 
stone  is  of  good  quality  the  strength  is  generally  very  much 
in  excess  of  any  probable  loads. 


BRICK. 

Brick  should  be  sound,  free  from  cracks  or  flaws,  stones,  or 
lumps.  They  should  be  of  uniform  size,  with  sharp  edges 
and  angles,  and  true  and  square  surfaces.  If  two  good  brick 
are  struck  together,  they  give  out  a  ringing  sound ;  while  if 
the  sound  is  dull,  the  brick  is  of  inferior  quality.  A  good 
brick  will  not  absorb  more  than  10  per  cent,  of  its  weight  of 
water;  the  best  will  not  absorb  over  5  per  cent.,  while  soft 
brick  will  take  up  from  25  to  85  per  cent. 

The  crushing  strength  of  good  quality  brick  should  not  be 


164 


MASONRY. 


less  than  4,000  lb.  per  sq.  in.  Most  good  brick  will  have  2  or  3 
times  this  strength.  The  weight  of  a  common  brick  is  about 
44  lb.,  or  118  lb.  per  cu.  ft.;  pressed  brick  of  the  same  size  will 
weigh  5  lb.  each,  or  131  lb.  per  cu.  ft. 

The  size  of  brick  is  variable,  as  shown  by  the  following 
table.  The  standard  brick,  adopted  by  several  associations  of 
builders  and  makers,  is  84"  X  4"  X  24"  for  common  brick,  and 
84"  X  41"  X  24"  for  face  brick. 


Size  of  Brick. 


Name. 

Thickness. 

Inches. 

Width. 

Inches. 

Length. 

Inches. 

Common  brick . 

2-24 

4 

84 

Philadelphia  pressed . 

24 

4 

8t% 

Peerless  Brick  Co . 

2f 

44 

84 

Baltimore  and  Trenton 

24 

44 

84 

Croton . 

24 

4 

84 

Colabaugh . 

24 

34 

84 

Maine  common . 

24 

34 

74 

North  River  common . 

24 

34 

8 

Milwaukee  . . 

24 

44 

84 

Stourbridge  firebrick . 

24 

44 

94 

TERRA  COTTA. 

All  pieces  of  terra  cotta  for  external  wTork  should  be 
tested  before  use.  They  should  emit  a  metallic  sound  when 
struck,  and  a  fracture  should  show  close  texture  and  uniform 
color.  The  surface  should  be  hard  enough  to  resist  a  knife 
scratch,  and  the  glazing  should  not  be  chipped  off.  Solid 
terra  cotta  weighs  about  120  lb.  per  cu.  ft.,  while  hollow  pieces 
of  ordinary  size  average  from  65  to  85  lb.  The  safe  working 
strength  of  terra-cotta  blocks  in  walls  is  about  5  tons  per 
sq.  ft.,  if  unfilled,  and  10  tons,  if  filled  solid  with  concrete. 


LIME. 

When  properly  burned,  quicklime  should  possess  the  fol¬ 
lowing  qualities :  It  should  be  in  lumps,  free  from  cinders, 
.  and  with  little  or  no  dust ;  it  should  slake  readily  in  water  to 


MATERIALS  OF  CONSTRUCTION. 


165 


a  smooth,  impalpable  paste,  without  residue ;  and  it  should 
dissolve  in  soft  water  if  enough  is  added. 

Lime  weighs  about  66  lb.  per  bu.,  or  about  53  lb.  per  cu.  ft. 
One  barrel  of  lime,  weighing  230  lb.,  will  make  about  2|  bbl., 
or  .3  cu.  yd.  of  stiff  paste.  In  l-to-3  mortar,  1  bbl.  of  unslaked 
lime  will  make  about  6£  bbl.  of  mortar  ;  or  1  bbl.  of  lime  paste 
will  make  about  3  bbl.  of  mortar.  For  a  l-to-2  mortar,  about 
1  bbl.  of  quicklime  to  5  or  5|  bbl.  of  sand  are  used. 


CEMENTS. 

The  two  kinds  of  hydraulic  cements  are  termed  Portland 
and  natural  (often  called  Rosendale,  from  a  place  in  . New 
York  where  much  of  it  is  made).  The  former  is  prepared  by 
mixing  together  suitable  proportions  of  clay  and  carbonate 
of  lime,  finely  pulverized,  and  burning  the  mixture  at  a  high 
heat  in  kilns,  after  which  the  mass  is  ground  to  a  fine  powder. 
Natural  cements  are  so  called  because  they  are  made  from 
the  natural  rock,  which  contain  the  clay  and  limestone  in 
the  proper  proportions.  • 

Portland  cements  are  dark  in  color,  weigh  from  90  to  100  lb. 
per  cu.  ft.,  are  very  slow  in  setting,  and  attain  great  ultimate 
strength.  Natural  cements  are  light  in  color,  weigh  from 
50  to  60  lb.  per  cu.  ft.,  are  very  quick  setting,  and  become 
from  i  to  |  as  strong  as  Portland  cement. 

A  barrel  of  Portland  cement  weighs  about  375  lb.  net ;  one 
of  the  Eastern  Rosendales,  300  lb.,  and  Western  Rosendales 
(from  Wisconsin,  Kentucky,  Illinois,  etc.),  about  265  lb.  A 
cubic  foot  of  slightly  compacted  cement  mixed  with  j  cu.  ft. 
of  water  will  make  from  f  to  f  cu.  ft.  of  paste ;  or  1  bbl.  of 
cement  will  make  about  3f  cu.  ft.  of  stiff  paste. 

Simple  Cement  Tests. — Mix  a  handful  of  the  cement  to  be 
tested  with  water,  and  make  it  into  two  cakes  about  £  in. 
thick,  with  thin  edges.  Let  one  dry  in  air  for  an  hour  and 
then  put  it  in  water  for  24  hours,  the  other  being  kept  in  air. 
If  at  the  expiration  of  that  tune  the  latter  has  become  quite 
hard,  and  when  broken  shows  considerable  tensile  strength, 
with  a  clean,  sharp  fracture,  without  crumbling,  and  the  cake 
in  water  retains  its  shape  and  has  become  much  harder,  such 


166 


MASONS  Y. 


a  cement  is  probably  amply  good  for  all  building  purposes. 
If  the  cake  kept  in  water  shows  bad  checks  or  cracks  on  the 
edges,  such  cement  is  unsafe  to  use  under  water,  for  any 
important  work.  If  the  sample  in  air  becomes  quite  hard, 
while  that  under  water  crumbles,  the  cement  may  often  be 
improved  by  mixing  about  half  as  much  slaked  lime  with  it. 
If  it  then  hardens,  it  may  be  used  in  wet  situations.  The 
rapidity  of  setting  in  air  may  often  be  retarded,  if  required, 
by  the  addition  of  a  small  quantity  of  slaked  lime.  A  cement 
which  remains  soft  in  air  and  does  not  become  hard  in  water 
in  24  hours,  may  be  a  good  cement  for  some  purposes,  but  is 
very  slow  setting  and  undesirable  for  use  in  damp  positions. 

Tensile  Strength. — When  a  testing  machine  is  available, 
tests  of  tensile  strength  of  cements  are  usually  made.  The 
following  table  indicates  the  average  strength  of  cemenl 
mortars  of  various  ages  and  compositions : 


Tensile  Strength  of  Cement  Mortars. 


Age  of  Mortar  When  Tested. 


Average  Tensile 
Strength.  Pounds 
Per  Square  Inch. 


Portland. 

Rosendale. 

Clear  Cement. 

Min. 

Max. 

Min. 

Max. 

1  day,  1  hour,  or  until  set,  in  air. . 

100 

140 

40 

80 

1  week . 

250 

550 

60 

100 

4  weeks  . 

350 

700 

100 

150 

1  year  . 

450 

800 

300 

400 

1  Part  Cement  to  1  Part  Sand. 

1  week . 

30 

50 

4  weeks . 

50 

80 

1  year . 

200 

300 

1  Part  Cement  to  S  Parts  Sand. 

1  week . 

80 

125 

4  weeks . 

100 

200 

1  year . 

200 

350 

All  samples,  except  the  first,  were  kept  in  air  1  day,  and 
the  remainder  of  the  time  in  water. 


MATERIALS  OF  CONSTRUCTION. 


167 


SAND. 

The  sand  should  he  sharp,  free  from  clay  or  earthy 
materials,  and  should  he  preferably  pit  sand.  Sea  sand 
should  never  be  used  unless  thoroughly  washed,  as  the  salt 
in  the  sand  causes  efflorescence,  and  the  cementing  material 
does  not  adhere  well  to  the  rounded  grains.  Pulverized 
brick,  cinders,  furnace  slag,  etc.  are  sometimes  used  as  sub¬ 
stitutes  for  sand  with  good  results.  The  addition  of  a  small 
quantity  of  brick  dust  to  ordinary  lime-and-sand  mortar 
seems  to  give  it  the  property  of  setting  under  water,  and  also 
prevents  disintegration  when  the  mortar  is  exposed  to  the 
elements.  _ 


MORTAR. 

In  mixing  lime  mortar,  a  bed  of  sand  is  first  made  in  a 
mortar  box,  and  the  lime  is  distributed  as  evenly  as  possible 
over  it,  both  lime  and  sand  being  previously  measured.  The 
lime  should  be  slaked  by  pouring  on  from  11  to  2  times  as 
much  water,  and  covered  with  a  layer  of  sand,  or  preferably, 
a  tarpaulin,  to  retain  the  vapor  given  off.  Sufficient  water 
should  be  used  at  the  start ;  if  more  must  be  added  later,  it 
chills  the  hot  lime  and  makes  it  lumpy.  Too  much  water 
makes  the  paste  thin,  weak,  and  slow  in  drying.  Additional 
sand  is  then  added,  if  necessary,  until  the  mortar  contains 
the  proper  proportion,  which  is  usually  3  of  sand  to  1  of  lime, 
although  2-to-l  is  much  better.  The  bulk  of  the  mortar  will 
be  about  \  greater  than  that  of  the  dry  sand  alone,  so  that 
20  cu.  ft.  or  16  bu.  of  sand,  and  4  cu.  ft.  or  3.2  bu.  of  quick¬ 
lime,  will  make  about  221  cu.  ft.  of  mortar. 

For  cement-and-lime  mortar,  the  materials  should  be  well 
mixed  together  before  water  is  added,  and  the  mortar  should 
be  used  before  the  cement  sets. 

A  good  method  of  mixing  cement  mortar  is  as  follows : 
One-half  the  quantity  of  sand  is  first  spread  over  the  bottom 
of  the  mortar  box ;  next,  the  cement  is  spread  evenly  over 
the  sand ;  and  the  remainder  of  the  sand  is  then  put  on. 
The  dry  materials  are  thoroughly  mixed  together,  either  by 
noe  or  by  shovel ;  water  is  then  added  to  so  much  of  the  mass 
as  is  required  for  immediate  use,  and  this  portion  is  mixed 


168  ' 


MASONRY. 


until  it  has  the  uniform  consistency  of  a  stiff  paste.  The 
quantity  of  water  required  depends  upon  the  cement  used, 
but  it  is  better  to  have  an  excess  than  a  deficiency.  Owing 
to  the  rapidity  of  setting,  only  small  lots  should  be  mixed  at 
a  time. 

In  winter,  a  small  proportion  of  lime  is  sometimes  mixed 
with  the  cement,  the  heat  generated  in  slaking  being  supposed 
to  prevent  freezing  until  the  cement  has  set.  Salt  is  often 
added  for  the  same  purpose,  the  quantity  being  about  1  lb.  of 
salt  to  18  gal.  of  water,  an  additional  ounce  being  added  for 
each  degree  of  temperature  below  32°  F.  Salt  is  objectionable, 
however,  as  it  causes  efflorescence. 


CONCRETE. 

Concrete  should  be  made  by  spreading  the  aggregate 
evenly  over  a  layer  of  cement  mortar  (made  as  described 
under  Mortar)  in  a  box  or  on  a  platform,  and  mixing  the 
materials  thoroughly.  The  aggregate  is  usually  broken  stone, 
not  over  a  specified  size ;  but  gravel,  broken  brick,  etc.,  may 
be  substituted.  Whichever  is  used  should  be  free  from  dirt, 
and  be  well  sprinkled  before  mixing.  The  pieces  should  be 
of  different  sizes,  so  that  the  smaller  pieces  will  fit  in  the 
spaces  between  the  larger. 

The  voids  in  broken  stone  are  one-half  the  bulk,  which 
space,  in  good  work,  is  practically  just  filled  by  the  mortar ; 
hence,  in  estimating  on  concrete,  it  is  necessary  to  figure 
about  as  much  broken  stone  as  there  are  to  be  cubic  yards  of 
concrete.  The  quantity  of  sand  will  be  about  one-half  cubic 
yard  per  yard  of  stone — when  gravel  is  not  also  used  ;  while 
the  cement  will  vary  according  to  proportions  required.  See 
table  on  page  170  giving  proportions  of  cement  and  sand  per 
cubic  yard  of  mortar. 

Probably  the  best  proportion  for  a  strong  concrete  is  1 
part  of  cement,  2  parts  of  sand,  and  4  or  5  parts  of  broken 
stone,  these  quantities  being  sufficient  to  fill  all  the  voids. 

A  very  good  concrete  may  be  made  by  using  the  follow¬ 
ing  quantities  of  materials,  which  when  mixed  will  make  1 
cu.  yd.:  2  bbl.  of  Rosendale  cement,  .5  cu.  yd.  of  sand,  and 


MATERIALS  OF  CONSTRUCTION. 


169 


.9  cu.  yd.  of  broken  stone.  The  mortar  alone  amounts  to 
.55  cu.  yd. 

A  concrete  nearly  as  strong  and  considerably  cheaper  is 
made  of  1  bbl.  of  Rosendale  cement,  2  bbl.  of  sand,  .5  cu.  yd. 
of  gravel,  and  .9  cu.  yd.  of  stone.  These  when  mixed  will 
make  1  cu.  yd.  The  mortar  amounts  to  .28  cu.  yd. 

In  laying,  concrete  should  not  be  dumped  from  a  consid¬ 
erable  height,  as  the  thoroughness  of  the  mixture  would  be 
destroyed.  It  should  be  spread  in  layers  of,  say,  8  in.  in 
thickness,  and  tamped  enough  to  compact  the  mass  well,  the 
surface  of  each  layer  being  left  rough,  to  form  a  better  bond 
with  the  succeeding  one. 

The  strength  of  concrete  increases  considerably  with  age. 
For  example,  a  Portland  cement  concrete  1  month  old  will 
crush  under  a  load  of  about  15  tons  per  sq.  ft.,  while  if  it  is  a 
year  old,  it  will  sustain  about  100  tons  per  sq.  ft.  These 
figures,  under  favorable  conditions,  may  be  nearly  doubled. 
Natural  cement  concretes,  with  various  proportions  of  mate¬ 
rials  and  of  ages  from  6  months  to  4  years,  showed  crushing 
strengths  of  from  70  to  100  tons  per  sq.  ft. 


QUANTITIES  OF  MATERIALS. 

Proportion  of  Mortar  in  Masonry. 


Kind  of  Masonry. 

Per  Cent,  of  Mortar. 

Minimum. 

Maximum. 

Brickwork,  coarse,  ¥'  to  f"  joints  ... 
Brickwork,  ordinary,  to  1"  joints 

35 

40 

25 

10 

30 

Brickwork,  pressed,  joints  . 

Ashlar,  courses  12"  to  20"  high,  joints 

15 

a"  y 

Ashlar,  courses  20"  to  32"  high,  joints 

7 

8 

to  |" . . 

5 

6 

Rubble,  coarse,  not  dressed  . 

33 

40 

Rubble,  roughlv  dressed . 

25 

30 

Rubble,  well  dressed,  coursed  . 

Concrete,  clean  stone,  without  grav- 

15 

20 

el  or  screenings . 

50 

55 

170 


MASONK  Y. 


Quantities  of  Materials  Per  Cubic  Yard  of  Cement 

Mortar. 


Proportions. 

Materials. 

Cement. 

Sand. 

Barrels  Cement  (Packed). 

Sand. 
Cu.  Yd. 

Portland  or 
Eastern  Rosendale. 

Western 

Rosendale. 

1 

0 

7.1 

6.4 

.0 

1 

1 

4.2 

3.7 

.6 

1 

2 

2.8 

2.6 

.8 

1 

3 

2.0 

1.8 

.9 

1 

4 

1.7 

1.5 

.95 

1 

5 

1.3 

1.1 

.97 

1 

6 

1.2 

1.0 

.98 

If  brickwork  is  figured  by  the  thousand  brick,  the  quanti¬ 
ties  of  cement  and  sand  obtained  by  aid  of  these  tables  should 
be  multiplied  by  either  2i,  2,  or  If,  according  to  whether  the 
brickwork  is  coarse,  ordinary,  or  pressed.  The  last  given 
figures  are  the  number  of  cubic  yards  which  1,000  standard 
size  brick  will  lay. 

As  a  perch  is  of  a  cubic  yard,  if  stonework  is  thus 
estimated,  the  figures  in  the  tables  may  be  used  for  perch 
measurement  by  deducting  from  the  final  results. 

Example.— How  many  barrels  of  Eastern  Rosendale 
cement  and  cubic  yards  of  sand  will  be  required  for  laying 
100  cu.  yd.  of  rubble  masonry  in  l-to-3  cement  mortar?  By 
the  first  table,  it  is  seen  that  the  minimum  percentage  of  mor¬ 
tar  in  coarse  rubble  is  33 ;  hence,  for  each  cubic  yard  of 
masonry  }  cu.  yd.  of  mortar  is  required.  According  to  the 
second  table,  a  l-to-3  mortar  requires,  per  cubic  yard,  2  bbl.  of 
cement  and  .9  cu.  yd.  of  sand  ;  or  1  cu.  yd.  of  rubble  requires  § 
bbl.  of  cement  and  .3  cu.  yd.  of  sand  ;  and  for  100  cu.  yd.  the 
quantities  are  07  bbl.  of  cement  and  30  cu.  yd.  of  sand. 

While  founded  on  actual  work,  the  above  tables  are  not 
intended  to  furnish  more  than  fairly  close  approximations, 
as  there  are  so  many  uncertainties  about  mortar  and  masonry 
that  very  accurate  estimates  cannot  be  made. 


FOOTINGS  AND  FOUNDATIONS. 


171 


FOOTINGS  AND  FOUNDATIONS. 

Before  beginning  a  structure,  the  character  of  the  soil 
should  be  investigated.  For  ordinary  work,  this  can  he  done 
by  boring— using  a  2"  auger— at  short  intervals,  around  the 
site.  The  auger  will  bring  up  samples  sufficient  to  determine 
the  character  of  the  soil.  This  is  a  useful  precaution,  but  can 
be  dispensed  with  for  the  usual  run  of  buildings,  the  bearing 
power  being  judged  by  experience  of  loads  in  adjacent  struc¬ 
tures,  or  by  examinations  of  near-by  excavations. 

Soils  may  be  classed  as  rock,  ordinary  soil,  and  made 
ground.  A  level  bed  of  rock  makes  the  best  possible  founda¬ 
tion  ;  sand  and  gravel  rank  next ;  clay  is  safe  for  moderate 
loads  if  kept  dry  ;  quicksand  should  be  removed  if  possible  ; 
and  soft,  marshy  ground  should  be  piled,  or  the  footings 
spread  enough  to  reduce  the  pressure  to  safe  limits.  Made 
ground,  usually  formed  of  garbage,  waste  earth,  etc.,  should 
not  be  built  on  for  important  structures,  without  tests  as  to 
its  bearing  power.  For  small  buildings,  however,  good  made 
ground  is  safe  to  build  on.  Table  XI,  page  74,  gives  the  loads 
which  different  kinds  of  soils  will  carry. 

If  water  is  encountered  in  excavating  foundations,  careful 
provision  must  be  made  for  its  removal  by  means  of  suitable 
drains.  The  ground  water  level  should  be  considered  also. 
Thus  a  building  may  have  a  good  foundation  on  wet  ground, 
until  the  water  is  drained  off,  by  excavation  of  deep  trenches 
in  the  street,  which  causes  settlement  in  the  foundation.  The 
frost  line,  or  depth  to  which 
ground  becomes  frozen,  must 
be  taken  into  account,  and  founda¬ 
tions  must  be  started  below  it ; 
otherwise  they  may  be  cracked  and 
heaved  out  of  place.  This  depth 
varies  from  3  ft.  to  6  ft.,  according 
to  the  severity  of  the  climate. 

Foundations  should  not  be  laid 
on  a  sloping  bed,  owing  to  the  lia¬ 
bility  of  slipping.  Nor  should  the 
walls  be  built  partly  on  rock  and 
partly  on  earth,  as  shown  in  Fig.  1,  for  the  weight  causes  the 


Fig.  1. 


172 


MASONRY. 


earth  to  settle,  and  the  wall,  being  carried  by  the  rock  only, 
would  be  unstable ;  or  water,  flowing  between  the  rock  and 
masonry,  and  freezing,  might  force  out  the  thin  wall.  When 
a  level  bed  cannot  be  otherwise  obtained,  concrete  may  be 
advantageously  used  for  this  purpose.  If  the  natural  surface 
is  rough,  the  better  will  concrete  adhere  to  it.  In  fact,  con¬ 
crete  should  be  used  much  more  than  it  is  for  foundation 
work.  For  buildings  of  moderate  weight,  erected  on  soft, 
clayey  soils,  the  bearing  power  of  the  latter  may  often  be  con¬ 
siderably  improved  by  spreading  layers  of  sand,  gravel,  or 
broken  stone,  and  pounding  it  into  the  soil.  Or,  the  soil  may 
be  compacted  by  driving  short  piles,  say  6  ft.  long  and  6  in. 
in  diameter,  as  close  together  as  necessary ;  from  2  to  4  ft. 
apart  is  generally  close  enough.  The  results  will  be  better  if 
the  piles  are  drawn  out  and  the  holes  filled  with  sand,  well 
compacted.  Thus  the  soil  is  consolidated,  and  the  sand, 
acting  as  so  many  small  arches,  transmits  the  load  to  the  sides 
of  the  hole,  as  well  as  to  the  bottom. 


PROPORTIONING  FOOTINGS. 


Footings  should  be  designed  for  the  load  they  are  to  carry, 
with  the  object  of  producing  a  uniform  settlement  in  all  parts 
of  the  building.  They  evidently  should  not  be  as  wide  under 
an  opening  as  under  a  solid  wall,  and  when  the  openings 


form  a  considerable  proportion  of  the  wall  area,  that  part  of 
the  footings  under  them  slxmld  be  omitted,  the  weight  being 
transmitted  by  arches  or  beams  to  the  footings  under  the 


FOOTINGS  AND  FOUNDATIONS. 


173 


sides  of  the  openings.  This  caution  is  very  important,  as  a 
majority  of  cracks  in  masonry  are  probably  due  to  continuous 
footings  where  little  or  none  are  needed.  If  one  portion  of  the 
foundation,  as,  for  example,  that  under  a  tower,  carries  much 
more  weight  than  another  part,  its  width  should  be  pro¬ 
portionately  increased. 

In  designing  footings, 
the  center  of  the  wall 
should  be  placed  verti¬ 
cally  over,  or,  prefer¬ 
ably,  a  little  inside  the 
center  of  the  base,  as 
sketched  in  Fig.  2 ; 
then  the  walls  will  be 
slightly  tilted  inwards, 
but  will  be  kept  in 
place  by  the  floor  joists, 
etc.  Where  there  are 
interior  piers,  these 
should  have  a  some¬ 
what  greater  load  per 
square  foot  —  that  is, 
less  area  per  toil  of 
load — than  the  walls, 
so  that  the  latter  will 
be  pressed  together, 
thus  preventing 
cracks ;  also,  as  the 
piers  usually  support 
iron  columns,  to  allow 
for  the  compression  in 
the  brickwork  joints, 
the  iron  being  practi¬ 
cally  incompressible. 

Footing  courses  should  be  battered  or  stepped  up,  making  the 
angle  abc  in  Fig.  3(a),  about  G0°.  The  load  then  becomes  well 
distributed  over  the  base.  If  the  footings  are  laid  as  shown  at 
(6),  the  projections  are  liable  to  break  off  at  the  edges  ot  the 
wall,  and  the  load  will  be  unevenly  carried  by  the  soil. 

L 


174 


MASONRY. 


To  show  the  method  of  proportioning  footings  (and  of 
figuring  loads  in  structures),  the  area  of  the  footings  for  a 
45'  X  60'  brick  warehouse,  shown  in  Fig.  4,  having  five 
stories  and  basement,  a  tar-and-gravel  roof,  tile  arch  floors, 
and  without  partitions,  will  be  determined.  There  are  two 
rows  of  columns,  spaced  14£  ft.  apart  longitudinally  and 
transversely.  The  walls  of  the  building  are  75  ft.  high,  25  ft. 
being  20  in.  thick,  and  50  ft.,  16  in.  thick.  As  the  basement 
floor  rests  directly  on  the  ground,  its  load  will  not  be  consid¬ 
ered.  The  floor  loads  on  the  first  and  second  stories  will  be 
taken  at  200  lb.  per  sq.  ft.,  and  on  the  others  at  150  lb. 

Assume  that  brickwork  weighs  120  lb.  per  cu.  ft.;  the  tile 
floor  80  lb.  per  sq.  ft.;  the  tar-and-gravel  roof  10  lb.  per  sq.  ft.; 
and  the  snow  load  at  12  lb.  per  sq.  ft.  Then,  for  each  foot  in 
length  of  the  side  walls,  the  load  is : 

Dead  Load. 

Walls— 

1  ft.  8  in.  X  1  ft.  X  25  ft.  =  41.7  cu.  ft. 

1  ft.  4  in.  X  1  ft.  X  50  ft.  =  66.7  cu.  ft. 

108.4  cu.  ft.  X  120  lb.  =  13,008  lb. 


Floors — 

(80  lb.  per  sq.  ft.  X  1  ft.  X  7*  ft. )  X  5  =  2,900  lb 

Roof- 

10  lb.  per  sq.  ft.  X  1  ft.  X  7*  ft.  =  72  lb. 

Live  Load. 

On  Floors — 

(200  lb.  per  sq.  ft.  X  1  ft.  X  7*  ft.)  X  2  =  2,900 

(150  lb.  per  sq.  ft.  X  1  ft.  X  7£  ft.)  X  3  ==  3,262  6,162  lb. 

Wind,  neglected  on  nearly  flat  roof  0  lb. 

Snow — 

12  lb.  per  sq.  ft.  X  1  ft.  X  7£  ft.  =  _ 87  lb. 


Total  dead  and  live  load  =  22,229  lb. 

Assume  that,  upon  testing,  the  soil  has  been  found  to  be 
moderately  dry  clay.  By  reference  to  page  74,  the  average 
safe  load  for  this  soil  is  found  to  be  3  tons  per  sq.  ft.  Hence, 
dividing  the  total  load,  22,229  lb.,  by  6,000  lb.,  there  results 
3f  ft.  as  the  approximate  width  of  the  footings  for  the  side 
walls.  If  the  foundation  walls  are  made  6  ft.  deep,  and  bat- 


FOOTINGS  AND  FOUNDATIONS. 


175 


tered  1  in.  per  foot,  the  top  width  will  he  2f  ft.  Thus  far  the 
weight  of  the  foundation  wall  has  not  been  considered.  Hay¬ 
ing  obtained  the  approximate  width  of  the  footing,  its  weight 
can  now  be  computed.  The  average  width  of  the  foundation 
wall  is  3  ft.  2  in.,  and  it  is  6  ft.  deep ;  the  contents  will  be  19 
cu.  ft.  per  foot  of  length  ;  the  walls  are  good  limestone  rubble, 
weighing  150  lb.  per  cu.  ft.,  so  that  the  total  weight  will  be 
2,850  lb.  Adding  this  to  22,229  lb.  and  dividing  by  6,000  lb., 
the  unit  load,  the  final  result  is  about  4}  ft.  as  the  width  of  the 
footing.  The  footings  for  the  end  walls  and  piers  may  be 
similarly  figured. 

Spread  Footings. — These  are  used  on  compressible  soils  to 
bring  the  load  per  square  foot  within  the  safe  bearing  power 
of  the  soil.  They  may  be  made  of  timber,  in  wet  soils,  alter¬ 


nate  courses  being  laid  transversely;  of  layers  of  I  beams  or 
rails,  laid  in  concrete ;  or  of  concrete  with  several  trans¬ 
verse  courses  of  twisted  iron  rods  (a  patented  method). 
These  are  shown  at  (a),  (5),  and  (c),  Fig.  5.  In  the  first  two 
cases,  it  is  necessary  to  figure  the  safe  length  of  the  projecting 
portion. 

For  example,  determine  the  size  of  the  timber  footing, 
Fig.  5  (a),  for  a  wall  having  a  load  of  40,000  lb.  per  ft.  in 
length.  The  ground  is  wet  and  not  safe  to  load  over  3,000  lb. 
per  ft.;  consequently,  the  footings  must  be  13}  ft.  wide.  Ihe 
stepped-out  foundation  is  32  in.  wide,  making  the  projection  L 
'  5  f t  4  in.  on  each  side.  To  find  what  size  timber  is  required, 


176 


MAS  ONE  Y. 


consider  either  side  as  ac,  a  cantilever  beam,  1  ft.  wide, 
uniformly  loaded,  supported  at  c,  and  resisting  the  upward 
reaction  of  the  earth  w  of  3,000  lb.  per  sq.  ft.;  for  5  ft.  4  in.  it 
is  L  w  =  16,000  1b.;  call  this  W.  According  to  Table  XXVI, 

page  113,  the  bending  moment  is  M  =  — —  =  — — - - 

Z  Z 


=  42,667  ft.-lb.;  or  512,000  in.-lb. 

The  resisting  moment  (see  page  114)  M\  =  QS,  S being  the 
safe  unit  fiber  stress,  and  Q  the  section  modulus,  which  for  a 

b  d2 

rectangular  beam  is,  from  Table  XII,  page  83,  —  —  ;  b  is  the 

width  and  d  the  depth.  Suppose  that  the  timber  is  spruce 

and  that  the  safe  bending  stress  is  1,000  lb.  per  sq.  in.;  let  the 

beam  be  12  in.  wide ;  its  depth  remains  to  be  determined. 

1,000  X  12  X  d2  .  ...  , 

Then,  Mi  = - - - .  Since  the  safe  resisting  moment 

6 


should  equal  the  bending  moment, 


Mi  =  M ,  or 


1,000  X  12  X  d2 
6 


=  512,000; 


whence,  d 


-]/  256  =  16  in. 


1512,000  X  6 
\  1,000  X  12 

Hence,  12"  X  16"  timbers,  set  side  by  side,  with  cross-layers 
of  planks  above  and  below,  shown  in  Fig.  5  (a),  would  be  used. 

The  principles  are  the  same  when  the  footing  consists  of  I 
beams,  or  rails,  but  other  values  are  used  for  Q  and  S,  on 
account  of  the  different  cross-sections  and  material.  (See 
page  118  for  rolled-steel  beams.)  The  safe  offsets  for  stone 
footings  may  also  be  figured  in  the  same  manner.  In  general, 
it  is  best  to  make  the  offset  in  each  course  of  stonework  or 
brickwork  not  greater  than  the  depth  of  the  course.  For  cal¬ 
culation  of  stone  beams,  as  flagstones,  lintels,  etc.,  see  page  119. 


PILES. 

When  piles  are  driven  closely  to  confine  puddle  in  a 
coffer  dam,  or  for  preventing  the  fall  of  an  earth  bank,  they 
are  called  shed  piles,  and  consist  of  planking  from  2  to  6  in. 
thick,  the  bottoms  being  cut  at  an  angle  which  forms  a 
driving  toe,  that  tends  to  keep  the  pile  close  up  to  the 


FOOTINGS  AND  FOUNDATIONS. 


177 


adjacent  one.  The  heads  are  kept  in  line  by  securing  longi¬ 
tudinal  stringers,  or  wales,  to  them  by  spiking  or  bolting. 

Piles  which  sustain  loads  are  called  bearing  piles.  They 
may  be  square  or  round  in  section,  but  are  usually  round, 
and  are  from  9  to  18  in.  in  diameter  at  the  top.  They  may  be 
used  either  with  or  without  the  bark.  White  pine  or  spruce 
is  suitable  where  the  ground  is  soft;  where  it  is  firmer, 
Georgia  pine  may  be  used  to  advantage.  Where  the  soil  is 
very  compact,  hard  woods,  such  as  oak,  hickory,  ash,  elm, 
beech,  etc.,  are  used.  Piles  are  usually  driven  at  intervals  of 
from  2i  to  4  ft.  between  centers,  according  to  the  nature  of 
the  soil  and  the  weight  to  be  sustained. 

The  following  formula  gives  the  safe  load  for  a  pile : 


in  which  W  —  safe  load  in  pounds ; 

io  ==  weight  of  hammer  in  pounds ; 
h  =  fall  of  hammer  in  feet ; 
k  =  penetration  of  pile  in  inches  at  the  last 
blow  (head  of  pile  in  good  condition,  not 
split  or  broomed). 

This  formula  gives  a  factor  of  safety  of  6.  Assuming  t  hat 
the  fall  of  the  hammer  is  30  ft.,  its  weight  2,000  lb.,  and  its 
penetration  at  the  last  blow  i  in.,  or  .5  in.,  the  safe  load  is 

2  X  2,000  X  30  _  120,000  _  goQOOlb.,  or  40  tons. 

.5  +  1  1-5 

Where  piles  are  spaced  at  3  ft,  between  centers  each  way, 
the  foundation  area  will  safely  sustain  a  load  of  from  3  to  5 
tons  per  sq.  ft.,  and  when  spaced  at  2.)  ft.  between  centers 
tach  way,  the  load  may  be  increased  to  from  5  to  7  tons  per 


sq-  ft-  ,  ,  ,, 

Where  the  soil  is  very  hard,  it  is  necessary  to  shoe  ie 
piles  with  cast  or  wrought  iron,  to  make  them  drive  more 
easily.  In  order  to  preserve  the  heads  from  brooming _an r 
splitting,  wrought-iron  hoops,  from  *  to  1  in.  thick,  and  2  or  o 


in.  wide,  are  used.  , 

When  driven,  the  piles  are  carefully  sawed  off  to  the  same 

level,  usually  below  the  water-line,  and  capped  by  cross-rows 
of  timbers  or  planking,  forming  a  grillage  upon  which  the 


178 


MASONR  Y. 


masonry  is  laid.  Sometimes  large  flat  stones  are  laid  directly 
on  several  of  the  piles.  This  method  is  good,  provided  the 
stones  are  set  so  as  to  bear  evenly  on  the  piles,  without  much 
pinning  up  by  spalls,  which  are  liable  to  be  crushed.  The 
heads  of  the  piles  may  also  be  embedded  in  concrete  for  2  or 
3  ft.,  which  makes  a  very  satisfactory  foundation. 


THICKNESS  OF  WALLS. 

Stone  foundation  walls  should  be  at  least  8  in.  thicker 
than  the  wall  above,  for  a  depth  of  12  ft.  below  grade  or  curb 
level ;  for  each  additional  10  ft.  or  part  thereof  in  depth,  they 
should  be  4  in.  thicker.  Thus,  if  the  first-story  walls  are 
12  in.,  the  foundation  should  be  20  in.  thick  if  12  ft.  deep,  and 
24  in.  thick  if  over  12  ft.  Stone  foundations  should  not  be 
less  than  16  in.  thick ;  a  thinner  wall  does  not  bond  well ; 
only  small  stones  can  be  used,  and  it  cannot  be  carried  to  any 
height.  The  thickness  of  foundation  walls  in  all  the  large 
cities  is  controlled  by  the  building  laws.  Where  there  are  no 
existing  laws,  the  following  table  will  serve  as  a  guide  : 


Thickness  of  Foundation  Walls. 


Height  of  Building. 

Dwellings, 
Hotels,  etc. 

Warehouses. 

Brick. 

Inches. 

Stone. 

Inches. 

Brick. 

Inches. 

Stone. 

Inches. 

Two  stories . 

12  or  16 

20 

16 

20 

Three  stories  . 

16 

20 

20 

24 

Four  stories . 

20 

24 

24 

28 

Five  stories . 

24 

28 

24 

28 

Six  stories  . 

24 

28 

28 

32 

The  table  on  page  179  is  a  tabulated  summary  of  the  New 
York  Building  Law  in  regard  to  walls,  and  may  be  safely 
taken  as  a  standard.  It  applies  only  to  buildings  having  solid 
masonry  walls,  and  not  to  those  of  skeleton-construction 
type,  in  which  the  walls  are  carried  on  the  framework. 


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FOOTINGS  AND  FOUNDATIONS. 


179 


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*If  brick  is  used,  width  may  be  4"  less.  For  foundations 
over  10'  deep,  thickness  must  be  increased  4  ior  each  addi¬ 
tional  10'  or  part  thereof.  .  c/, 

f  Non-bearing  partition  walls,  less  than  oO  high,  may  be  <  . 
j  If  clear  span  is  over  27 ,  all  bearing  walls  must  be  4 
thicker  for  each  12*'  over  27  span. 


180 


MASON  11 Y. 


For  heights  greater  than  those  given,  the  lower  part  must  he 
4"  thicker  for  each  25'  or  fraction  thereof  in  height,  the  upper 
115'  or  100',  respectively,  remaining  as  given  in  table. 


MASONRY  CONSTRUCTION. 


NOTES  ON  STONEWORK. 

Stone  being  the  stronger  material,  a  wall  should  have  as 
much  stone  and  as  little  mortar  as  possible.  Contact  of  the 
stones  in  bed  joints  is  not  advisable,  as  the  shrinkage  of 
the  mortar  may  leave  them  bearing  only  on  the  projecting 
angles.  The  thickness  of  joints  in  stonework  is  from  T3S  to  £ 
or  $  in.,  depending  on  the  class  of  work ;  but  for  ordinary 
ashlar,  the  usual  thickness  is  about  |  in.,  and  more  in  rough 
masonry.  Bed  joints  should  be  full  and  square  to  the  face, 
as  if  worked  slack  at  the  back — to  make  thin  face  joints — 
spalls  are  likely  to  break  off  at  the  front  edges.  Good  bond¬ 
ing  is  essential  for  a  strong  wall,  and  the  proper  placing  of 
headers  should  be  carefully  watched.  Long  pieces  of  stone 
should  be  well  supported  and  bedded  to  prevent  breaking ; 
pieces  more  than,  say,  four  times  the  thickness,  should  not  be 
used.  Stone,  especially  if  stratified,  should  be  laid  on  its 
natural  or  quarry  bed,  as  if  set  vertically,  water  easily  pene¬ 
trates  between  the  layers,  and,  freezing,  splits  off  the  outer 
ones.  For  damp  places,  stonework  (and  brickwork)  should 
be  laid  in  cement  mortar  or  lime-and-cement  mortar,  while 
in  dry  positions  good  lime  mortar  may  be  used.  In  laying 
stone,  the  mortar  should  be  kept  back  about  an  inch  from  the 
face  of  the  wall ;  otherwise  spalls  may  be  broken  off,  owing 
to  the  outside  mortar  hardening  more  rapidly  than  that  in 
the  interior,  settlement  bringing  the  pressure  on  the  hard 
layer.  This  precaution  is  very  important  in  the  case  of  lug 
sills,  band  courses,  etc.  The  joints  may  be  pointed,  after  the 
wall  is  built,  with  some  non-staining  mortar. 

The  value  of  grouted  walls  is  a  much  disputed  point.  A 
wall  grouted  with  thin  lime  mortar  undoubtedly  requires  a 
long  time  to  dry  thoroughly,  while  if  the  grout  is  thick,  it 


MASONR  Y  CONS TR  UCTION. 


181 


does  not  fill  every  crevice.  With  cement  grout,  however,  a 
wall  so  filled  is  very  much  stronger  than  one  laid  with  stiff 
mortar,  as  has  been  shown  by  tests.  When  using  cement 
grout,  the  brick  or  stone  should  not  be  wet ;  they  will  then 
absorb  the  water  in  the 
grout,  and  also  some  of 
the  cement,  thus  increas¬ 
ing  the  adhesion.  Grout 
is  usually  made  of  ordi¬ 
nary  mortar,  thinned  to 
the  consistency  of  cream. 

If  an  extra  strong  wall  is 
required,  a  1-to-l  mortar 
may  be  used. 

Ashlar  should  be  care¬ 
fully  bonded,  either  by 
using  courses  of  different  pIG  g 

thickness,  or,  if  the  ashlar 

is  only  from  2  to  4  in.  thick,  by  means  of  wire  ties  and 
anchors,  such  as  are  shown  in  Fig.  11.  When  the  courses  are 
from  4  to  8  in.  thick,  a  good  bond  to  the  backing  may  be  had 

by  using  each  thickness  in 
alternate  courses.  When  the 
backing  'is  brick,  the  joints 
in  it  should  be  as  thin  as 
possible  ;  and  if  lime  mortar 
is  used,  some  cement  should 
be  added,  to  prevent  shrink¬ 
age.  Very  thin  ashlar  must 
not  be  considered  in  deter¬ 
mining  the  strength  of  walls, 
but  the  backing  must  be 
made  sufficiently  strong,  in¬ 
dependent  of  the  ashlar. 

All  projecting  courses, 
such  as  cornices,  lintels,  sills,  etc.,  should  be  beveled  on  top, 
and  have  a  drip  cut  on  the  under  side,  as  shown  at  a,  Fig.  fi, 
to  prevent  water  from  soaking  into  the  joints.  Lug  sills 
should  only  be  beveled  between  the  jamb  lines,  the  ends 


182 


MAS  ONE  Y. 


being  cut  level,  as  at  b,  thus  keeping  out  water  from  the 
joint  between  brick  and  stone,  and  also  forming  a  more 
secure  bearing  for  the  wall.  The  top  of  exposed  walls 
should  be  covered  by  coping,  in  long  pieces,  and  have 
the  vertical  joints  well  filled  with  good  mortar.  Gable  co¬ 
pings  should  be  anchored  very  firmly,  either  by  iron  dowels 
or  ties,  or  by  bond  stones,  the  latter  method  being  shown 
in  Fig.  7. 


CLASSES  OF  STONE  MASONRY. 

Rubb|e  Masonry. — This  is  used  for  rough  work,  such  as 
foundations,  backing,  etc.,  and  although  frequently  consist¬ 
ing  of  common  field  stone,  quarried  stone  should  be  used 
where  possible,  as  better  bonding  and  bedding  can  be 
secured. 

At  (a),  Fig.  8,  is  shown  a  common-  or  random-coursed 
rubble  wall,  in  which  the  stones  are  bonded  every  three  or 
four  feet,  as  at  a.  The  angles  are  laid  with  large  well-shaped 
stone,  the  long  sides  alternating ;  in  the  body  of  the  wall  the 
stones  are  set  irregularly,  the  interstices  in  the  heart  of  the 
wall  being  filled  with  spalls  and  mortar. 

At  ( b )  is  shown  cobweb  rubble,  which  is  used  for  suburban 
work.  The  quoins,  or  corner  stones,  are  hammer-dressed  on 
top  and  bottom,  but  may  be  rock-faced.  All  the  joints  should 
be  hammer-dressed  and  no  spalls  should  show  on  the  face, 
while  the  joints  should  not  be  thicker  than  i  in.  This  class 
of  work  is  more  expensive  than  common  rubble. 

At  (c)  is  shown  a  rubble  wall  with  brick  quoins.  In  this 
work  all  the  horizontal  joints  have  hammer-dressed  level 
beds.  This  makes  a  good  wall  and  can  be  built  cheaply 
when  the  stone  used  splits  readily. 

At  ( d )  is  shown  regular-coursed  rubble.  In  this  work 
continuous  horizontal  joints  are  run  at  intervals  of  15  to 
18  in.  in  the  height,  as  at  a  b  c  and  d  ef.  No  attention  need  be 
paid  to  uniformity  of  height  in  the  different  courses,  but  the 
beds  should  be  made  as  nearly  parallel  as  possible. 

Ashlar. — When  the  outside  facing  of  a  wall  is  of  cut  stone, 
it  is  called  ashlar,  regardless  of  the  manner  in  which  the 
stone  is  finished. 


MASONR  Y  CONS  TR  UCTION. 


183 


Regular-coursed  ashlar,  shown  at  (e),  Fig.  8,  has  pieces 
uniform  in  height  and  the  courses  continuous.  Stones  about 
12  in.  high  and  from  18  to  24  in.  long  are  the  cheapest,  both 
as  to  first  cost  and  in  expense  of  handling.  The  illustration 


shows  the  stone  hush-hammered  with  tooled  draft  lines.  A 
good  effect  is  produced  by  making  the  courses  of  two  differ 
ent  heights,  as  shown  at  (/),  the  courses  a  being  from  10  to 
18  in  high  and  composed  of  “  facers,”  while  the  courses  b  are 


184 


MASONRY. 


from  5  to  7}  in.  high  and  constitute  binding  courses.  The 
latter  should  be  at  least  4  in.  wider  than  the  thickest  stones 
used  in  the  facing  courses. 

Random ,  or  broken-range,  ashlar  consists  of  blocks  truly 
squared  but  of  different  sizes,  forming  a  broken  range  or 
course.  As  this  masonry  is  in  itself  irregular;  it  is  well 
adapted  to  buildings  of  irregular  plan  or  of  irregular  sky 
line.  Random  ashlar  is  finished  in  various  ways.  The 
simplest,  though  not  the  least  effective,  finish  is  the  plain 
rock  face,  shown  in  ( g ).  The  block  must  first  be  cut  true 
and  square  all  around,  forming  beds  and  vertical  joints,  after 
which  straight  lines  are  drawn  around  the  edges,  about  2  in. 
from  the  face  of  the  block.  A  wide  pitching  chisel  is  then 
used  along  these  lines,  knocking  off  the  surplus  material. 
The  smallest  stone  used  should  not  be  less  than  4  in.  in  height, 
nor  the  largest  greater  than  16  in.  The  bond,  or  the  lap  of 
one  stone  over  another,  should  be  at  least  6  in.  for  the 
smaller  stones  and  8  in.  for  the  larger.  The  length  of  any 
block  should  not  be  less  than  1£,  nor  more  than  4,  times  its 
height.  The  hardest  kinds  of  rock  are  best  suited  for 
masonry  of  this  sort,  which  is,  perhaps,  the  most  common 
kind  of  ashlar  used  in  modern  building. 


STONE  FINISHES. 

Some  of  the  tools  used  in  making  the  finer  finishes  for 
stonework  are  shown  in  Fig.  9.  The  crandall  (a)  consists  of 
a  wroxight-iron  bar,  flattened  at  one  end,  with  a  slot, 
f  in.  wide  and  3  in.  long,  in  which  ten  double-headed  points, 
made  of  square  steel  about  9  in.  long,  are  fastened  by 
means  of  a  key.  It  is  used  to  finish  the  surface  of  sandstone 
after  it  has  been  worked  with  the  tooth-axe  or  chisel. 
The  patent  hammer  (b),  made  of  several  thin  blades  of  steel, 
ground  to  an  edge  and  held  together  with  bolts,  is  used 
for  finishing  granite  or  hard  limestone.  The  bush  hammer 
(c),  from  4  to  8  in.  long  and  2  to  4  in.  square,  has  its 
ends  cut  in  pyramidal  points.  This  hammer  is  used  for 
finishing  limestone  and  sandstone  after  the  surface  has  been 
made  nearly  even. 


MASONRY  CONSTRUCTION. 


185 


Fig.  9. 


186 


MASONRY. 


At  (d)  is  shown  the  appearance  of  rock-faced  or  pitch¬ 
faced  work.  The  face  of  the  stone  is  left  rough,  just  as  it 
comes  from  the  quarry,  and  the  edges  are  pitched  off  to  a 
line.  Rock-faced  finish  is  cheaper  than  any  other  kind,  as 
but  little  work  is  required. 

At  (e)  are  shown  two  kinds  of  crandalled  work ;  that  on  the 
left  shows  the  appearance  when  the  lines  run  all  one  way, 
while  that  on  the  right  shows  the  lines  crossing.  This  finish 
is  very  effective  for  the  red  Potsdam  and  Longmeadow  sand¬ 
stones. 

At  (/)  is  shown  broached  work,  in  which  continuous 
grooves  are  formed  over  the  surface. 

At  ( g )  is  shown  bush-hammered  work,  which  leaves  the 
surface  full  of  points.  This  finish  is  very  attractive  on 
bluestone,  limestone,  and  sandstones,  but  should  not  be  used 
on  softer  kinds. 

At  (/i)  is  shown  pointed  work  ;  that  on  the  left  half  of  the 
stone  being  rough-pointed,  while  the  right  half  is  fine-pointed. 
In  the  rough-pointed  work,  the  point  is  used  at  intervals  of 
one  inch  over  the  stone,  while  in  the  fine-pointed,  the  i>oint  is 
used  at  every  half  inch  of  the  surface. 

At  (i)  is  shown  the  patent-hammered  finish,  generally  used 
on  granite,  bluestone,  and  limestone.  The  stone  is  first 
dressed  to  a  fairly  smooth  surface  with  the  point,  and  then 
finished  with  the  patent  hammer.  The  fineness  of  the  work 
is  determined  by  the  number  of  blades  in  the  hammer.  For 
U.  S.  government  work,  10  cuts  per  inch  are  generally  specified, 
but  8  cuts  per  inch  is  good  work. 

At  (j)  is  illustrated  tooled  work.  For  this  finish,  a  chisel 
from  3  to  4£  in.  wide  is  used,  and  the  lines  are  continued 
across  the  width  of  the  stone  to  the  draft  lines. 

At  (k)  is  shown  vermiculated  work,  so  called  from  the 
worm-eaten  appearance.  Stones  so  cut  are  used  in  quoins  and 
base  courses.  This  dressing  is  very  effective,  but  expensive. 

At  ( l )  is  shown  droved  work,  similar  to  tooled  work,  except 
that  the  lines  are  broken,  owing  to  the  smaller  size  of  the 
chisel  used.  It  is  less  expensive  than  tooled  work. 

When  a  smooth  finish  is  desired,  the  surface  of  the  stone  is 
rubbed.  This  is  best  done  before  the  stone  becomes  seasoned. 


MASONRY  CONSTRUCTION. 


18? 


BONDS  IN  BRICKWORK. 

In  Fig.  10  are  shown  the  three  principal  bonds  in  brick¬ 
work.  In  (a)  is  shown  English  bond,  consisting  of  alternate 
courses  of  stretchers  and  headers.  The  longitudinal  bond  is 
obtained  by  means  of  either  one-quarter  bats,  as  shown,  or 
preferably  by  three-quarter  bats.  This  bond  is  probably  the 
strongest  and  best  one,  although  not  much  used.  In  ( b )  is 
shown  Flemish  bond,  consisting  of  alternate  headers  and 
stretchers  in  the  same  course.  The  lap  is  obtained  by  use  of 
three-quarter  bats,  with  quarter,  half,  and  three-quarter  inte¬ 
rior  closers.  In  (c)  is  shown  the  ordinary  bond,  which  consists 
of  5  or  6  courses  of  stretchers  to  each  course  of  headers.  This 
bond  is  not  as  strong  as 
the  first  two  named,  as 
there  is  a  continuous  ver¬ 
tical  joint  extending  be¬ 
tween  the  header  courses. 

From  (a)  to  ( i ),  Fig.  11, 
are  shown  methods  of 
bonding  face  brick  to  the 
backing  in  both  solid  and 
hollow  walls ;  also  of 
bonding  terra-cotta  fur¬ 
ring  to  walls.  At  (j), 

(k),  and  (l)\ are  shown 
methods  of  joining  old 
and  new  walls;  ( j ) 
shows  a  vertical  groove 
cut  in  the  old  wall  to 
form  a  sliding  joint  with 
the  new  wall;  (k),  a  2" 

X  4"  piece  spiked  to  the 
old  wall  for  the  same 
purpose ;  and  ( l ),  a  steel- 
tie  bond  (also  adapted 
for  bonding  face  brick) . 

In  Fig.  12  are  shown  methods  of  tying  face  brick  to  the 
woodwork  in  brick-veneered  walls  by  means  of  steel  ties,  etc. 


188 


MASONRY. 


MASONRY  CONSTRUCTION  DURING  EXTREMES  OF 

TEM  PERATU  RE. 


Extremes  of  heat  or  cold  are  both  unfavorable  to  the  union 
of  the  building  material  and  the  mortar. 


MASONRY  CONSTRUCTION. 


189 


Extreme  heat  causes 
quick  evaporation  of  the 
water  in  mortar,  leaving 
the  mortar  in  practically 
the  same  condition  as  be¬ 
fore  mixture.  This  effect 
is  intensified  by  the  very 
dry  condition  of  the  stone 
or  brick,  which  readily 
absorbs  moisture  from  the 
mortar.  In  hot  weather 
the  surfaces  of  the  brick 
and  stone  are  covered  with 
dust,  which  is  very  detri¬ 
mental  to  adhesion,  and 
should  be  removed  before 
using  the  material.  The 
mortar,  whether  lime  or 
cement,  should  be  thinner 
than  usual,  and  the  brick 
and  stone  should  be  well 
sprinkled  before  laying. 
When  built,  the  wall 
should  be  frequently 
sprayed  with  water,  to 
lower  its  temperature,  and 
prevent  excessive  evapor¬ 
ation. 

In  making  concrete,  the 
sand  and  gravel  should  be 
well  washed,  and  kept 
moist  by  liberal  spraying ; 
where  practicable,  a  tem¬ 
porary  cover  over  the 
work,  to  keep  off  the  sun’s 
rays,  should  be  provided. 

In  plastering,  similar 
points  require  attention ; 
the  openings  in  the  build- 


in 


190 


MASONR  Y. 


ing  should  be  closed,  to  prevent  hot-air  currents  from 
extracting  moisture  too  rapidly  from  the  plaster.  Where 
patent  plaster  is  used,  the  dry  lathing  should  be  well  mois¬ 
tened  before  the  mortar  is  applied,  and  care  must  be  exer¬ 
cised  that  the  coats  do  not  become  dry  before  the  subsequent 
ones  are  applied.  Hard  plasters  are  not  injured  by  frost 
after  they  have  begun  to  set,  but  should  be  protected  from  it 
for  the  first  36  hours  after  application. 

Extreme  cold  prevents  the  setting  of  mortar  by  freezing 
the  moisture  in  it,  and  also  by  forming  films  of  ice  on  the 
brick  or  stone.  If  lime  mortar  is  to  be  used  during  freezing 
weather,  rich,  newly  slaked  lime,  thoroughly  well  mixed, 
gives  good  results,  as  it  retains  much  of  the  heat  of  slaking. 
With  hydraulic  cement  the  set  takes  place  more  rapidly,  and, 
if  well  begun,  frost  does  not  apparently  injure  the  mortar ; 
the  particles  in  combining  expel  the  excess  of  moisture ;  a 
much  closer  contact  is  thus  secured,  and  the  mortar  is  denser. 
Although,  in  appearance,  the  work  may  not  have  suffered 
from  the  action  of  frost  on  the  cement,  many  experiments 
have  conclusively  shown  that  cement  rnoBtar  after  freezing 
loses  as  much  as  one-third  the  tensile  strength  it  possesses 
when  not  frozen. 

In  order  to  lower  the  freezing  point,  a  solution  containing 
2  or  3  per  cent,  of  salt  is  mixed  in  the  mortar,  reducing  the 
temperature  of  freezing  about  5° ;  that  is,  until  the  ther¬ 
mometer  registers  below,  say,  28°,  the  operations  are  safe.  It 
has  been  conclusively  proved,  however,  that  the  addition  of 
salt  to  cement  is  injurious  to  its  strength,  as  the  crystalliza¬ 
tion  of  the  salt  creates  a  force  opposing  adhesion,  and  tends 
to  disintegrate  the  particles ;  salt  also  attracts  moisture,  thus 
making  the  walls  constantly  wet. 

The  top  of  the  walls  should  be  kept  covered  when  work 
is  stopped,  so  that  rain  may  not  enter  and,  freezing,  sepa¬ 
rate  the  constituent  parts  of  the  masonry.  Sheets  of  tar¬ 
paulin  or  roofing  felt  are  most  convenient  for  the  purpose. 
When  the  temperature  has  reached  the  freezing  point,  it  is 
unsafe  to  dress-cut  unseasoned  stone  in  the  open  air,  as  the 
quarry  sap  in  the  stone  freezes,  and  the  stone  may  be  frac¬ 
tured  during  the  process  of  cutting. 


MASONRY  CONSTRUCTION. 


191 


WATERPROOFING  WALLS. 

Damp  cellar  walls  are  due  either  to  water  soaking  through 
from  the  outside,  or  to  wet  bottoms,  from  which  water  rises 

in  the  walls  by  capillary  action. 
The  decay  of  vegetable  matter  con¬ 
tained  in  dirty  water  generates  gases 
injurious  to  health,  so  that  the  pre¬ 
vention  of  dampness  in  walls  is  a 
point  of  great  importance.  Provision 
must  be  made  to  convey  the  water 
away  from  the  walls,  as  well  as  to 
make  the  latter  damp-proof.  No 
earth  should  be  placed  against  the 
wall,  a  12"  or  18"  space  next  to  it 
being  filled  with  broken  stone  or 
gravel,  with,  if  practicable,  an  open- 
jointed  tile  drain  laid  at  the  bottom, 
as  shown  in  Pig.  13.  The  outside  of 
Hff  the  walls  and  footings  should  be 
plastered  thickly  with  1-to-l  cement 
mortar  ;  or,  preferably,  with  asphalt 
and  coal  tar,  mixed  in  the  proportion  of  9  to  1,  and  applied, 
while  hot,  about  f  in.  thick  to  the  dry  walls.  The  asphalt 
course  should  also  extend  through  the  walls,  as  shown  at  the 
under  side  of  the  concrete  floor,  which  should  be  3  or  4  m. 
thick,  and  laid  on  a  6"  or  8"  bed  of  broken  stone.  In  place 

of  concrete,  a  very  durable  composition,  made  of  60  parts  of 

hot  asphalt,  10  of  coal  tar,  and  30  of  sand,  may  be  use  . 

The  ascent  of  moisture  in  walls  may  be  prevented  by 
inserting  on  the  footing  course  two  courses  of  roofing  sat  or 
very  hard  brick,  laid  with  broken  joints  m  cement  mortar, 
or  a  few  layers  of  tarred  felt  may  be  used. 

Efflorescence.— Efflorescence,  or  the  white  coating  frequently 

seen  on  outside  of  stonework  and  brickwork,  is  caused  by 
the  deposition  of  soluble  matter  in  the  mortar,  whic^be  g 

dissolved  in  the  water  used  in  mixing  is  deposited  u^.n  the 

surface  of  the  wall,  as  the  water  evaporates.  This  efflorescence 
may  be  removed  by  washing  the  walls  With  a  elution .  at 
muriatic  acid  in  20  parts  of  water.  When  clean  and  dry  the 


Fig.  13. 


192 


MASONRY. 


walls  may  be  coated  with  a  preservative;  one  of  the  commonest 
being  boiled  linseed  oil,  which,  applied  in  2  coats,  and,  when 
dry,  washed  over  with  weak  ammonia,  will  be  effectual  for  2 
or  3  years  before  needing  renewal.  Lead  and  oil  paint  is  some¬ 
times  used,  but  is  objectionable,  as  it  changes  the  color  of  the 
masonry,  and  also  flakes  off.  Cabot’s  brick  preservative  is 
used  to  waterproof  brick  and  sandstone,  and  is  effectual  where 
the  heart  of  the  wall  is  kept  dry. 

Sylvester’s  process,  which  has  proved  quite  successful, 
and  is  simple  in  preparation  and  application,  consists  of  two 
washes,  the  first  being  made  of  Castile  soap  and  water,  in  the 
proportion  of  £  lb.  of  soap  per  gallon  of  water,  and  the  second 
of  $■  lb.  of  alum  per  gallon.  The  soap  wash  is  applied,  boiling 
hot,  with  a  brush,  to  the  clean  and  dry  walls,  and  allowed  to 
dry  24  hours  before  the  alum  wash — which  need  not  be  hot — 
is  put  on  in  the  same  manner.  The  coats  are  applied  alter¬ 
nately  2  or  3  times,  making  the  wall  practically  impervious. 

All  ordinary  cements  will  cause  efflorescence,  and  when 
such  are  used  in  stonework,  the  face  stones  should  be  set 
entirely  with  Yicat,  Lafarge,  or  some  other  non-staining 
cement  mortar,  mixed  with  sand  in  the  proportion  of  1  to  2. 
If  this  method  be  too  expensive,  the  joints  of  the  stonework 
may  be  raked  out  to  a  depth  of  1  in.,  and  pointed  with  a 
mortar  made  with  one  of  these  cements.  Good  lime  mOrtar 
is  often  used  in  setting  ashlar,  and  by  some  is  claimed  to  be 
practically  as  good  for  the  purpose,  and  considerably  cheaper 
than  the  cements  named. 


CHIMNEYS  AND  FIREPLACES. 

Chimneys. — In  planning  chimneys,  the  points  to  be  consid¬ 
ered  are  the  height,  and  the  number,  size,  and  arrangement 
of  the  flues.  Attention  must  also  be  given  to  the  location  in 
respect  to  valleys,  etc.  on  the  roof.  To  make  the  chimney 
‘  draw  ”  properly,  a  separate  flue  should  be  provided,  extend¬ 
ing  from  each  fireplace  to  the  top  of  the  chimney.  For  ordi¬ 
nary  stoves  and  small  furnaces,  the  flues  may  be  8 in.  X  8  in.; 
but  if  the  furnace  is  large,  it  is  better  to  make  the  flue 
8  in.  X  12  in.,  and  the  same  size  should  be  used,  when  possible, 
for  fireplaces  having  large  grates.  (See  Fireplaces.)  Flues 


MASONE  Y  CONSTR  UCTION. 


193 


are  sometimes  only  4  in.  wide ;  but  are  then  easily  choked 
with  soot  and  difficult  to  clean,  so  that  a  flue  should  not  be 
less  than  8  in.  wide.  Flues  should  always  be  lined  with 
some  fireproof  material ;  in  fact,  the  building  laws  of  large 
cities  so  require.  The  lining  is  usually  fireclay,  tile,  or  gal- 
vanized-iron  pipe.  If  the  pipe  used  is  round,  the  space 
between  it  and  the  Avails  of  the  chimneys  may  be  utilized  for 
ventilation.  The  outer  walls  of  chimney  flues  should  be  8  in. 
thick,  if  flue  linings  are  not  used.  Whenever  it  is  necessary 
to  change  the  direction  of  the  flue,  the  diversion  should  be 
effected  by  long  curves,  and  not  by  sharp  turns,  which  retard 
the  passage  of  smoke.  Chimneys  should  extend  above  the 
highest  point  of  the  building  or  of  those  adjoining;  other¬ 
wise  they  are  likely  to  smoke.  This  may  be  obAdated,  when 
the  chimney  is  not  carried  high  enough,  by  using  a  hood 
having  two  open  sides ;  but  as  hoods  are  unsightly,  their  use 
should  be  avoided,  when  possible.  The  top  of  a  chimney 
should  be  covered  by  a  stone  slab,  either  solid,  to  prevent  the 
entrance  of  rain — the  smoke  passing  out  through  holes  at  the 
sides  near  the  top — or  with  a  hole  the  size  of  the  flue  cut  in  it, 
preventing  disintegration  of  the  exposed  mortar  joints. 

Fireplaces. — The  general  construction  of  a  fireplace  is  shown 
in  Fig.  14.  The  projection  in  the  room  is  called  the  chimney 
breast,  and  its  width  a  is  generally  5  ft.,  Avhich  is  the  standard 
Avidth  for  ordinary  fireplaces,  the  return  b  in  this  case  being 
17  in.  The  height  of  the  fireplace  opening  at  c  is  about  30  in. 
from  the  finished  floor  line  to  the  springing  line  of  the  arch, 
the  rise  of  which  may  be  3  or  4  in.  The  width  of  the  opening 
betAveen  the  rough  bricks,  as  d,  should  be  25  or  26  in.,  and 
the  depth  of  the  niche  e,  from  12  to  13  in.  These  measure¬ 
ments  may  be  adjusted  to  suit  special  grates  and  fittings. 

The  arrangement  of  the  floor  framing  requires  no  explana¬ 
tion,  other  than  that  the  trimmer  joists  should  be  kept  2  in. 
from  the  brickAVork.  A  temporary  Avooden  center  supports 
the  brick  trimmer  arch  during  construction.  The  space  above 
the  arch  is  leAreled  up  Avith  cement  concrete,  upon  which  is 
laid  the  slate  or  tile  hearth.  With  this  method  of  construct¬ 
ing  a  fireplace,  it  is  almost  impossible  for  the  woodAvork  to 
catch  fire. 


194 


MASONRY. 


The  opening  above  the  fireplace,  or  throat,  is  gradually 
contracted  to  the  size  of  the  flue  lining,  as  shown  at  l  and  to. 
Several  courses  of  brick  are  corbeled  out  from  the  back,  as 
at  n ;  on  the  ledge  formed  is  placed  a  sliding  iron  damper.  A 


preferable  form  of  construction  consists  in  the  insertion,  just 
below  the  throat  l,  of  a  tilting  damper,  which  may  be  operated 
by  a  key  placed  in  the  front  of  the  fireplace. 

A  good  proportion  for  flues  of  fireplaces  in  which  it  is 
intended  to  burn  wood  or  bituminous  coal,  is  to  make  the 
sectional  area  of  the  flue  that  of  the  fireplace  opening,  if 
the  flue  is  rectangular,  and  TV  if  the  flue  is  circular  ;  thus,  for 
a  fireplace  which  is  30  in.  wide  X  30  in.  high,  or  900  sq.  in.  in 
area,  the  area  of  a  rectangular  flue  would  be  90  sq.  in.,  which 
is  nearly  equivalent  to  an  8"  X  12  "  flue  ;  for  a  circular  flue  it 
would  be  75  sq.  in.,  which  is  equivalent  to  a  10"  flue.  When 
anthracite  coal  is  to  he  used  in  the  fireplace  grates,  the  flue 
area  may  he  made  that  of  the  fireplace  opening  for  the 
rectangular  form,  and  for  the  circular. 


- a- 

Fig.  14. 


MASONRY  CONSTRUCTION. 


195 


CEMENT  WALKS  AND  FLOORS. 

Where  the  curb  is  not  already  in  place,  stakes  should 
be  set  to  grade  and  to  aline  either  edge  of  the  walk,  the 


other  being 
obtained  h  y 
leveling  over, 
taking  care  to 
allow  an  out¬ 
ward  pitch  on 


Fig.  15. 


the  surface  of  about  1  in.  per  ft.  Straight-edged  strips  should 
be  nailed  to  the  inside  of  each  line  of  stakes,  with  top  edges 
level  with  them,  to  form  the  mold  for  the  concrete.  The 
ground  should  he  leveled  off  about  10  in.  below  the  finished 
grade  of  the  walk,  and  well  settled  by  ramming,  as  at  d,  Fig.  15. 
A  foundation  a,  5  in.  thick  should  then  be  laid,  of  either  coarse 
gravel,  stone  chips,  sand,  or  cinders,  well  tamped  or  rolled. 
The  concrete  should  have  the  proportions  of  1  part  of  cement, 
2  parts  of  sand,  and  5  or  6  parts  of  gravel,  mixed  dry  ;  then  a 
sufficient  quantity  of  water  is  added  to  make  a  stiff  mortar. 
This  concrete  should  he  spread  in  a  layer  from  3  to  4  in.  thick, 
as  at  b,  and  should  he  well  tamped.  Before  it  has  set,  the 
finishing  coat  c  should  he  laid,  and  only  as  much  concrete 
should  be  laid  as  can  he  covered  with  cement  the  same  day, 
for  if  the  concrete  gets  dry  on  top,  the  finishing  coat  will  not 
adhere  to  it.  The  top  coat  should  consist  of  equal  parts  of 
the  best  Portland  cement  and  sand,  or  clean,  finely  crushed 
granite  or  flint  rock,  mixed  dry,  water  being  then  added  to 
give  the  consistency  of  plastic  mortar.  It  should  be  applied 
with  a  trowel,  to  the  thickness  of  1  in.,  and  be  carefully 
smoothed  and  leveled  flush  with  the  tops  of  the  guides.  It  is 
best  to  mark  off  the  Avalk  into  squares,  etc.,  by  grooves  }  or 
|  in.  deep,  so  that  in  case  it  should  crack,  the  fractures  will 
follow  the  grooves  and  not  disfigure  the  whole  walk.  In  hot 
weather,  the  cement  should  not  be  allowed  to  dry  too  rapidly, 
but  should  be  sprinkled  occasionally.  Usually  a  walk  is 
ready  for  use  in  from  24  to  30  hours  after  completion,  and  the 
forms  may  then  he  removed. 

The  same  general  methods  above  described  apply  to 
cemented  cellar  floors. 


198 


MASONRY. 


Fig.  16. 


MASONR  Y  CONSTR  UCTION. 


197 


198 


MAS 0 NR  Y. 


HANGERS,  CAPS,  ANCHORS,  ETC. 

The  use  of  joist  and  girder  hangers,  etc.  simplifies  greatly 
the  work  of  framing  both  for  house  and  mill  construction. 
With  these  hangers  a  good  bearing  and  firm  support  for  the 
joists,  girders,  etc.  may  be  had,  and  in  case  of  fire  the  timbers 
may  give  way  without  injury  to  the  masonry. 

At  (a),  (5),  and  (c),  Fig.  1G,  are  shown  the  ordinary  forms 


Fig.  18. 

of  wrought-iron  stirrups,  or  hangers;  at  (d),  (e),  and  (/)  are 
shown  joist  hangers  for  use  in  frame  buildings;  at  ( g ),  ( h ), 
( i ),  and  (j)  hangers  for  use  in  brick  walls.  At  ( k )  is  repre¬ 
sented  a  hanger  for  heavy  girders  or  joists,  adjustable  to  suit 
several  sizes  of  timber  by  changing  the  bearing  plate  a,  thus 
serving  the  same  purpose  as  that  shown  at  (7),  which  repre¬ 
sents  a  hanger  made  in  right  and  left  parts,  and  fastened 


MAS  ONE  Y  CONSTRUCTION. 


199 


together  by  a  bolt.  Of  the  hangers  shown,  (c£),  (g),  (k)  are 
the  Van  Dorn  ;  (e),  (h),  (i),  (j),  (0. the  DuPlex  5  and  the 
Goetz,  types. 

At  (a),  (b),  and  (c),  Fig.  17,  are  represented  2-member  post 
caps ;  one  is  steel  and  the  others  are  cast  iron.  At  (d)  and  (e) 
are  shown3-mem- 
ber  post  caps ;  at 
(/),  (flO.  and  (h)t 
one  steel  and  two 
cast-iron  4-mem¬ 
ber  post  caps.  At 
(i)  and  (j)  are 
shown  two  cast- 
iron  wall-bearing 
plates;  at  (k),  a 
steel  wall-plate 
hanger;  at  (Z),  a 
cast-iron  box 
anchor  for  use 
over  a  1  edged 
wall ;  at  (m),  (n), 
and  ( o ),  cast-iron 
bar  anchors,  the 
latter  for  I  beams. 

At  (p)  is  shown  a 
steel  base  plate, 
and  at  ( q )  and 
(r),  two  forms  of 
cast.-iron  base 
plates.  The  caps, 

fa)'' and  (p),  are  the  Van  Dorn ;  and  those  at 

anchor1 passes  t'hrongh  the  ’wall,  as  at  (<t>,  a  cast-iron  washer, 
0^gh5ar:"iSenns  of  ties  for  anchoring  ! 


Fig. 19. 


200 


MASONRY. 


beams,  channels,  etc.;  (a),  (b),  ( c ),  and  (d)  represent  ordi¬ 
nary  wall  anchors ;  (e)  is  a  tie-rod  anchor  running  through 
the  wall,  and  (/)  shows  the  upper  I  beams  connected  by  a 
flsh-plate  and  secured  to  the  girder  by  dips. 

When  wall  boxes  or  hangers  are  not  used,  templets,  or 
bearing  stones,  should  be  placed  under  the  ends  of  beams 
and  girders,  to  distribute  the  weight  evenly  on  the  wall. 
They  should  be  of  tough  stone,  having  a  thickness  of  about  1 
the  least  surface  dimension,  but  not  less  than  4  in.  It  is  weL 
to  place  flat  stones  above  the  joists,  etc.,  so  that  any  shrinkage 
in  the  latter  will  not  affect  the  wall.  The  building  laws  of 
some  cities  provide  that  joists  shall  be  supported  on  corbels, 
at  least  4  in.  wide.  This  is  a  good  construction,  but  a  cornice 
is  required  to  conceal  the  corbel. 


ARCHES. 

The  general  forms  of  arches  are  semicircular,  segmental, 
pointed,  elliptical,  etc.,  the  name  being  determined  by  the 

Voussoir  curve  of  the  intra- 

dos,  or  inner  curve 
of  the  arch.  The 
outer  curve  is 
termed  the  extra- 
dos.  The  soffit  is 
the  concave  surface 
of  the  arch.  Vous¬ 
soir  s  or  ring  stones 
are  the  pieces  com¬ 
posing  the  arch,  the 
center  or  highest  stone  being  termed  the  keystone  or  kcy- 
block.  The  first  courses  at  each  side  are  called  springers, 
except  in  the  case  of  segmental  arches,  in  winch  they  are 
termed  skewbacks.  The  voussoirs  between  the  skewbacks  or 
springing  stones  and  the  keystone  collectively  form  the  flanks 
or  haunches,  and  t  he  spandrels  are  those  portions  of  the  wall 
above  the  haunches  and  below  a  horizontal  line  through  the 
crown  of  the  extrados. .  See  Fig.  20. 

The  span  is  the  horizontal  distance  between  jambs,  and 


ARCHES. 


201 


the  perpendicular  distance  from  the  springing  line  to  the 
highest  part,  or  crown,  of  the  soffit  is  the  rise. 

The  joints  of  circular  and  segmental  arches  radiate  from 
a  single  center.  In  arches  having  two  or  more  centers,  the 
'oints  in  each  arc  of  the  curve  radiate  from  their  respective 
centers.  The  joints  of  elliptic  arches  are  found  thus :  Draw 
lines  from  each  of  the  several  points  (spaced  off  on  the  intra- 
dos  or  extrados)  to  the  foci,  as  shown  at  («),  Fig.  21 ;  bisect 
ihe  angles  thus  formed,  and  the  bisecting  lines  will  give  the 
direction  of  the  joints.  The  joints  in  flat  arches  are  drawn 
from  the  vertex  of  an  equilateral  triangle  having  the  spring¬ 


ing  line  as  a  base.  ,  .  ,  , 

Examples. — At  (a),  Fig.  21,  is  shown  a  semicircular  arch, 

of  which  a  &  is  the  springing  line  and  c  d  the  rise. 

At  (6)  is  shown  a  segmental  arch ;  the  center  a  is  taken  on 
the  line  ab,  which  bisects  the  span  cd.  The  radius  of  this 
arch  equals  approximately  the  square  of  the  span  divided  by 
eight  times  the  rise.  For  exact  formula,  see  Sector,  page  o7. 

At  (c)  is  shown  a  Moorish ,  or  horseshoe,  arch,  the  springing 
line  ab  being  below  the  center  from  which  the  curve  is 
struck  making  a  sweep  of  about  230  degrees.  A  similar  form 
is  the  pointed  Moorish  arch,  differing  from  (c)  only  above  the 
line  cd,  above  which  it  takes  the  form  of  a  iwo-centercd  or 
pointed  arch.  These  two  arches  are  called  stilted  arches,  from 
the  fact  that  the  center  is  raised  above  the  springing  me. 

Another  example  of  stilted  arch  is  shown  at  (d  ,  m  which 
the  arch  centers  are  on  the  line  a  6,  and  the  springing  line  c  d 

'S  AtWfe  shown  a  fiat  arch  built  of  wedge-shaped  voussoirs 
together  serving  as  a  lintel ;  the  joints  radiate  from  a  center 
at  the  vertex  of  an  equilateral  triangle  of  winch  the  span  is 

0D  A n/>  is  rre"e  abtweTby  this  construction 

rheZ^:^  —  £  own  weight  and  that  of  the 

“£  wstu  rs  - 


202 


MASONRY. 


1 


the  same  length  us  the  springing  line  be.  At  (/;)  is  shown 
an  arch  in  which  the  centers  are  taken  inside  the  jamb  lines, 


ARCHES. 


203 


thus  flattening  the  arch  ;  in  this  example,  the  radius  is  equal 
to  '$  of  the  span.  At  (  i)  is  shown  a  pointed  arch  having  the 
span  a  b,  and  the  height  c  d,  which  is  greater  than  the  span. 
To  find  the  centers,  proceed  as  follows:  Draw  the  line 
a  d,  and  bisect  it  by  ef,  which  cuts  the  springing  line  at  /,  on 


JL^- 

CT 

f\  \ 

IT 

pK 

&/ 

1 

«  4  dl 

\ 

\\ 

\v 

ft  b 

■0 

// 

(m) 


-ft 

c 

g 

(nj 

Fig.  21.  (6.) 

ab  produced.  Then,  with/ as  cen¬ 
ter  and  a  radius/ a,  one  side  of  the 
arch  may  be  drawn,  the  other  half  . 

being  similarly  found. 

At  O')  and  (k)  are  shown  examples  of  Jour-centered 
Gothic,  commonly  called  Tudor,  arches.  At  O')  is  repre¬ 
sented  an  arch  in  which  the  given  span  a  b  is  divided  into  six 
equal  parts,  as  at  c,  d,  e,  etc.  To  find  the  centers  for  the 
longer  radii,  with  c  and  e  as  centers,  and  a  radius  ce,  describe 
arcs  intersecting  at/;  draw  Jc  and  fe,  and  produce  these 


204 


MASONRY. 


lines  to  g ,  A,  i,  and  j ;  the  last  two  points  will  he  the  required 
centers.  With  c  and  e  as  centers,  and  a  radius  c  a,  describe 
arcs  a  g  and  b  h ;  with  i  and  j  as  centers,  and  a  radius  i  A, 
describe  the  arcs  h  k  and  g  k. 

At  ( k )  is  shown  an  arch  of  similar  construction,  but  the 
span  a  6  is  divided  into  four  equal  parts.  The  distances  a  c 
and  b  d  are  each  made  equal  to  a  b ;  lines  are  then  drawn 
from  c  and  d  through  e  and  /  and  produced  to  g  and  A ;  the 
arcs  are  then  struck  in  a  manner  similar  to  that  shown  at  (j ). 

At  ( l )  is  represented  an  ogee  arch,  which  is  stilted  one 
part  in  seven  of  the  total  height.  The  span  is  divided  into 
six  equal  parts,  and  the  centers  for  the  lower  arcs  are  taken 
at  a  and  b,  at  each  side  of  the  center  line  c  d ;  the  arcs  are 
tangent  on  the  outer  line  of  the  molded  architrave,  the  posi¬ 
tion  of  e  and  /  being  determined  by  the  width  of  the 
neck  at  g. 

At  (m)  is  shown  a  three-centered  arch  having  the  span  a  b 
given.  To  lay  out  this  arch,  divide  a  b  into  four  equal  parts, 
as  at  cde;  from  a  and  b  as  centers,  with  a  radius  a e,  describe 
the  arcs  ef  and  e/,  intersecting  on  the  center  line  fg. 
From  c  and  e  as  centers,  with  a  radius  c  a,  describe  the  arcs 
ah  and  bi;  and  from  /  as  a  center,  with  the  radius /A, 
describe  the  arc  A  g  i,  completing  the  figure. 

At  (o)  is  shown  a  three-centered  skew  arch,  which  closely 
approaches  an  elliptic  curve  in  form.  To  construct  the 
arch,  having  given  the  required  span  a  b  and  the  height  c  d, 
proceed  as  follows :  Take  any  point  e  on  c  d,  and  make  aj 
and  g  b  equal  to  e  d.  Draw  / e,  and  bisect  this  line  by  the 
line  A  i,  cutting  the  center  line  d  c  at  A.  Draw  A/A  and  A  gj ; 
vith/  and  g  as  centers,  draw  the  arcs  a  k  and  bj ;  and  with  A 
as  a  center,  draw  the  arc  k  dj. 

At  (p)  is  represented  a  form  of  arch  used  for  egg-shaped 
sewers.  To  lay  out  the  curves,  draw  the  springing  line  a  b 
and  the  center  line  d  e ;  from  /  and  g  as  centers,  with  a  radius 
g  c,  describe  arcs  cutting  the  springing  line  in  a  and  b ;  with 
these  points  as  centers,  and  a  radius  af,  describe  the  arcs /A 
and  g  i.  Divide  the  span  g  f  into  four  equal  parts  by  points/  c, 
and  k,  and  from  the  points  a  and  b  as  centers,  with  a  radius  a  k, 
describe  arcs  intersecting  the  center  line  d  e  at  the  point  l ; 


ARCHES. 


205 


now,  with  l  as  the  center,  and  a  radius  l  h,  describe  the  arc  h  e  i ; 
draw  the  upper  curve  g  df,  which  is  a  semicircular  arc  struck 
from  the  common  center  c,  thus  completing  the  figure. 

To  construct  a  rampant  arch  (such  as  is  used  for  carry¬ 
ing  a  flight  of  stone  steps),  as  shown  in  Fig.  22,  the  base  line  a  b 
and  the  angle  of  inclination  being  given,  draw  ab  to  the 
required  length,  and  at  a  lay  off  the  angle  of  inclination ; 
draw  the  line  a  c ;  bisect  it,  and  at  the  points  a,  bJ  and  c  erect 
the  lines  ad,b  e,  and  f  g  h,  each  perpendicular  to  a  b.  Now, 
through  h — a  point  on  the  under  side  of  the  arch  determined 
by  the  thickness  required  for  the  step  backing  and  voussoirs — 
draw  a  line  d  e  parallel  to  a  c,  completing  the  rhomboid 
adec.  Divide  the 
line  ac  into  any 
number  of  equal 
parts,  and  divide  a  d 
and  c  e  into  one-hal  f 
as  many  equal  parts. 

From  h  draw  lines 
to  the  points  on  ad 
and  ce  just  found  ; 
make  gf  equal  to 
g  h,  and  from / draw 
lines  through  the 
points  on  the  line 
a  c,  producing  them 
to  intersect  those 
first  drawn,  as  at  j,  etc.  These  points  then  will  be  on  the 
required  curve,  which  may  be  readily  traced  through  them. 
To  locate  the  axes  and  foci  of  the  ellipse,  erect  ck  perpendic¬ 
ular  to  a  c  at  c,  and  make  it  equal  in  length  to  g  h.  W  itli  g  as 
a  center,  and  a  radius  gk,  describe  an  arc  intersecting  ec  at  l , 
a  line  drawn  from  l  through  the  center  g  will  give  im  as  the 
major  axis;  and  no,  perpendicular  to  it  at  g,  will  be.  the 
minor  axis.  Taking  the  distance  g  m  as  the  radius,  and  with  n 
as  the  center,  describe  arcs  cutting  the  major  axis  at  v  and  p ; 
these  points  will  be  the  foci  of  the  ellipse,  and,  alter  maiking 
the  thickness  of  the  joints  on  the  intrados,  the  joint  lines 
may  be  drawn  as  explained  for  (?i),  Fig.  21. 

N 


206 


MASONRY. 


RETAINING  WALLS. 

A  retaining  wall  is  a  wall  built  to  rebut  the  pressure  of 
earth,  either  wet  or  dry.  In  designing  such  a  wall  it  is  neces¬ 
sary  to  ascertain  the  character  of  the  material  to  be  retained. 
If  the  latter  is  rock,  the  wall  evidently  need  not  be  as  thick 
as  if  the  material  were  wet  clay,  and  would  be  merely  a  face 
wall. 

Any  granular  material,  when  unconfined,  spreads  out  to 
its  natural  slope,  termed  technically  the  angle  of  repose,  which 

varies  with  the  material  and  also 
with  the  quantity  of  moisture  in  it. 
The  slope  usually  taken  in  engi¬ 
neering  work,  as  being  safe  for 
nearly  all  kinds  of  earth,  is  1£  ft. 
horizontal  to  1  ft.  vertical,  corre¬ 
sponding  to  an  angle  of  33°  42'. 
The  pressure,  then,  which  a  retain¬ 
ing  wall  sustains,  is  evidently  the 
weight  of  the  prism  of  earth  in¬ 
cluded  between  the  back  face  of 
the  wall  a  b,  Fig.  23,  and  the  plane  b  c,  inclined  to  the  hori¬ 
zontal  at  the  angle  of  repose  of  the  material — the  earth 
having  a  level  top  surface.  The  amount  and  direction  of 
this  pressure  are  indeterminate,  and  so  many  varying  factors 
enter  into  the  problem  that  no  attempt  will  be  made  to  explain 
the  theory  of  retaining  walls,  and  only  a  few  practical  points 
will  be  touched  on  respecting  their  design. 

There  is  considerable  diversity  of  practice  in  the  propor¬ 
tioning  of  retaining  walls.  Most  authorities,  however,  agree 
that  the  base  should  be  from  .3  to  .5  of  the  height,  the  latter 
ratio  being  the  greatest  required  under  any  but  the  most 
unusual  conditions. 

The  following  proportions  represent  very  safe— but  not 
excessive — construction :  In  Fig.  24,  let  a  h  =  1 ;  then  g  k 
*=  .4 ;  a  b  =  £ ;  g  h  —  5  cd,  ef,  etc.  =  from  9  to  12  in.  each, 

the  distance  i  k  being  divided  up  so  as  to  make  steps  of  about 
these  widths.  For  example,  let  ah  =  16  ft.;  then  g k  —  16 
X  .4  =  6.4  ft.,  say  6  ft.  6  in.;  gh  =  ^  of  16  ft.  =  1  ft.  4  in.; 
ab  =  £  of  16  ft.  =  2ft.  8  in.;  cd,  etc.  =  ( gk  —  gi)  -h  3  =  lOin. 


Fig.  23. 


RETAINING  WALLS. 


207 


The  preceding  proportions  are  not  intended  to  apply  in 
their  entirety  to  small  walls  less  than  about  6  ft.  high ,  in 


such  cases  steps  are  usually  unneces¬ 
sary,  and  the  top  width  should  not  be 
less  than  18  in.,  so  that  the  wall  may 
be  sufficiently  thick  to  withstand  the 
action  of  frost  on  the  backing.  A  wall 
designed  as  above  indicated  will  be 
amply  strong  to  retain  a  considerable 
surcharge,  or  bank,  of  earth  sloping 
back  above  the  top  of  the  wall.  Area 
walls  that  are  supported  at  short  in¬ 
tervals  by  cross-walls,  beams,  etc.  do 
not  need  to  be  as  thick  as  retaining 
walls  which  have  no  such  bracing. 

The  masonry  courses,  while  usu¬ 
ally  laid  horizontally,  should  prefer¬ 
ably  be  laid  sloping  towards  the 
embankment,  to  lessen  the  liability  of 
slipping,  and  should  be  started  below 
the  frost  line.  The  stones  should  be 
as  large  as  possible,  bonding  and 


r-iah- 


-4ah- 

Fig.  24. 


breaking  joints  both  longitudinally  and  transversely, 
built  of  brick,  the  bond  should  be  the  same  as  stone  with 
broken  joints,  wherever  possible,  to  make  the  wall  a  homo¬ 
geneous  mass.  The  back  should  be  left  rough,  to  increase 
the  friction  between  the  wall  and  the  backing,  and 
the  work  progresses, 'it  should  be  coated  thickly  with  hot 
cml  tar  or  other  waterproof  material,  as  a  precaution  against 
tvater  soaking  in.  Above  thefrost  level,  on  the  upper  surface 
"l Ihe  emhankment,  the  back  of  the  wall 
tered  sharply  up  to  ^  “^^Tupon  tim  backing. 

T^preventthe^cumulaUorfo^water  at  the  back  of  the  wall, 

oor^  drain  tiles  should  be  laid  at  proper  levels  along  the 
k  i  tiin  Wall  to  collect  all  surface  and  rift  w ater,  and  dis 
f  tt  lme  tough  small  openings,  called  weepers,  left 
^  wallTor  ".rpose.  The  natural  drainage  of  the 
soil  never  should  be  dammed  up  by  a  wall. 


208 


CARPENTRY  AND  JOINERY. 


CARPENTRY  AND  JOINERY. 


WOODS  USED  IN  BUILDING. 

White,  or  Northern,  pine  is  a  light,  soft,  straight-grained  wood, 
and  is  used  in'  building  principally  as  a  finishing  material 
where  a  good  but  inexpensive  job  is  required.  Its  power  of 
holding  glue  renders  it  valuable  to  the  joiner. 

Georgia  pine,  also  known  as  hard  pitch,  or  long-leafed,  pine, 
has  a  dense  dark  color,  and  well-marked  grain,  on  account  of 
which  it  is  sometimes  used  as  a  finishing  material.  The  wood 
is  heavy,  hard,  strong,  and,  under  proper  conditions,  very  dura¬ 
ble,  but  decays  rapidly  in  damp  places.  On  account  of  its 
resinous  nature  it  does  not  take  paint  well.  Georgia  pine  is 
often  confused  with  Carolina,  yellow,  or  Southern  pine,  which 
is  greatly  inferior  to  it. 

Loblolly  pine,  sometimes  called  Texas  pine,  has  a  close  resem¬ 
blance  to  Georgia  pine,  but  is  of  coarser  grain,  softer  in  fiber, 
and  grows  more  sap-wood.  It  is  largely  used  in  the  Southern 
states  for  framework  and  interior  finish. 

Oregon  pine,  sometimes  called  Washington  fir,  while  really 
belonging  to  the  spruce  family,  so  closely  resembles  pine  that 
it  is  so  called.  While  nearly  as  strong  as  Georgia  pine,  it  is 
much  lighter  in  weight,  and  more  easily  worked.  Owing  to 
the  long  lengths  in  which  it  can  be  obtained  it  is  in  demand 
for  flagstaffs  and  long  framing. 

Black  spruce,  growing  in  the  Southern  states  and  Canada, 
is  light  in  weight,  reddish  in  color,  and  though  easy  to  work, 
is  very  tough  in  fiber.  It  is  largely  used  for  submerged  cribs 
and  piles,  as  it  not  only  preserves  well  under  water,  but  also 
resists  the  destructive  action  of  parasitic  Crustacea. 

White  spruce,  scarcely  distinguishable  from  black,  is  largely 
used  throughout  the  Eastern  states  for  all  classes  of  lathing, 
framing,  and  flooring. 

Norway  spruce  has  a  tough,  straight  grain  which  makes  it  an 
excellent  material  for  masts  of  ships,  etc.  Under  the  name  of 
white  deal  it  fills  the  same  place  in  European  woodworking 
shops  as  white  pine  does  in  America. 


WOODS  USED  IN  BUILDING. 


209 


Red  spruce,  growing  in  the  Northeastern  portion  of  the 
United  States  and  in  Canada,  is  similar  to  black  spruce. 

Hemlock  is  like  spruce  in  appearance,  but  much  inferior 
in  quality,  is  brittle,  splits  easily,  and  liable  to  be  shaky. 
It  is  only  used  as  a  cheap,  rough  framing  timber. 

White  cedar,  a  soft,  light,  fine-grained,  and  very  durable 
wood,  lacking  strength  and  toughness,  is  much  used  for 
boat-building,  cigar-box  manufacture,  shingles,  and  tanks. 

Red  cedar,  a  smaller  tree  than  white  cedar,  similar  to  it 
in  texture  but  more  compact  and  durable,  is  of  a  reddish- 
brown  color,  and  possesses  a  strong,  pungent  odor,  which 
repels  moths  and  other  insects,  making  it  extremely  valuable 
as  shelving  for  closets,  and  linings  for  chests  and  trunks. 

Cypress,  a  wood  very  similar  to  cedar,  growing  in  the 
Southern  part  of  both  Europe  and  the  United  States,  is  one  of 
the  most  durable  woods,  and  well  adapted  for  outside  or 
inside  work.  Special  care  must  be  taken  in  seasoning  it,  as  it 
tends  to  sliver  and  become  shaky  if  forced  in  the  drying. 

Redwood,  the  name  given  to  one  of  the  species  of  giant 
trees  of  California,  grows  to  a  height  of  from  200  to  300  ft., 
its  trunk  being  bare  and  branchless  for  one-third  of  its 
height.  The  color  is  a  dull  red,  and  the  wood,  resembling 
pine,  is  used  in  the  West  the  same  as  pine  is  in  the  East.  As 
an  interior  finish  it  is  capable  of  taking  a  high  polish,  and 
its  color  improves  with  age. 

White  oak  is  the  hardest  of  the  American  oaks,  and  grows 
in  abundance  throughout  the  eastern  half  of  the  United 
States.  The  wood,  heavy,  hard,  cross-grained,  strong,  and  of 
a  light  yellowish-brown  color,  is  used  where  strength  and 
durability  is  required,  as  in  cooperage  and  carriage  making. 

Red  oak  is  darker  and  redder,  coarser,  more  brittle,  and 
of  a  more  porous  texture  than  white  oak. 

English  oak,  though  similar  to  American  oaks,  is  superior 
to  them  for  such  structural  purposes  as  ship  building  and 
house  framing. 

Oak  is  especially  prized  as  a  material  for  cabinetwork, 
when  the  log  is  quarter-sawed.  In  first-class  work,  it  is 
usually  cut  into  veneers  T3C  in.  thick,  which  are  laid  on 
cores  of  white  pine  or  chestnut.  The  silver  grain  and  the 


210 


CARPENTRY  AND  JOINERY. 


high  polish  that  the  wood  is  capable  of  receiving  make  it  one 
of  the  most  beautiful  used  in  joinery. 

Hickory  is  the  hardest  and  toughest  of  American  woods, 
and,  owing  to  the  difficulty  in  working  it,  is  very  little  used 
as  a  building  material.  Hickory  is  also  attacked  by  boring 
insects.  This  wood  possesses  great  flexibility,  and  hence  is 
valuable  for  carriages,  sleighs,  and  implements  requiring 
bent-wood  details.  1 

Ash,  the  wood  of  a  large  tree  growing  in  the  colder  portions 
of  the  United  States,  is  heavy,  hard,  and  very  elastic.  Its 
grain  is  coarse,  and  very  much  like  bastard-sawed  oak  in 
appearance.  Ash  is  sometimes  used  for  cabinetwork,  but  its 
tendency  to  become  decayed  and  brittle  renders  it  unfit  for 
structural  work.  The  white  ash  is  exceedingly  tough,  and  is 
largely  used  for  interior  trim.  It  closely  resembles  white 
oak,  and  when  properly  filled  can  be  brought  to  a  high 
polish.  Black  ash  has  a  brown,  cedar-like  appearance. 

Locust  is  one  of  the  largest  forest  trees  in  the  United  States, 
and  furnishes  a  wood  that  is  as  hard  as  white  oak.  It  is 
composed  of  very  wide  annual  layers,  in  which  the  vessels 
are  few  but  very  large  and  are  arranged  in  rows,  giving  the 
wood  a  peculiar  striped  grain.  Its  principal  use  is  in  exposed 
places  where  great  durability  is  required.  As  its  hardness 
increases  with  age,  it  is  used  for  turned  ornaments  and 
occasionally  in  cabinetwork. 

Black  walnut  is  heavy,  hard,  porous,  and  of  a  purplish  color, 
marked  by  a  beautiful  wavy  grain.  Strong,  durable,  and  not 
subject  to  the  attacks  of  insects,  it  is  used  generally  for  small 
cabinetwork,  gun  stocks,  and  interior  decoration.  The 
knotted  roots  of  the  tree  furnish  material  with  a  curly  grain, 
called  burl,  which  is  cut  up  into  veneers. 

Cherry. — The  wood  of  the  wild  cherry  is  moderately  heavy, 
hard,  very  durable,  and  has  a  close,  fine  grain.  It  is  suscep¬ 
tible  of  a  high  polish,  and  is  much  used  for  fine  interior  trim 
and  cabinetwork.  Cherry  stained  black  to  imitate  ebony 
cannot  be  detected,  except  by  scraping  the  polished  surface. 
It  is  largely  used  for  piano  cases,  furniture,  etc. 

Birch  strongly  resembles  cherry  in  texture,  and  in  some 
species  in  color  also.  Black  or  cherry  birch  furnishes  the  best 


WOODS  UbED  IN  BUILDING. 


211 


lumber,  but  is  not  as  durable,  and  is  more  affected  by  atmos¬ 
pheric  influences. 

Maple  is  a  light-colored,  fine-grained,  strong,  and  heavy 
wood.  The  medullary  rays  are  small  and  distinct,  giving 
a  silver  grain  to  the  quarter-cut  lumber.  It  is  used  for 
flooring  and  interior  trim,  but  for  fine  work  it  is  used  as 
veneers.  Curly  maple  is  maple  in  which  the  waviness  of  the 
grain  is  similar  to  that  obtained  from  the  roots  of  the  walnut 
tree.  Bird's-eye  maple  is  produced  in  old  trees  by  the  circular 
inflection  of  the  fibers.  Though  both  the  curly  maple  and 
the  bird’s-eye  are  practically  distorted  fibers,  and  reduce  the 
strength  of  the  wood,  they  are  highly  prized  in  the  cabinet¬ 
maker’s  art. 

Chestnut  is  comparatively  soft,  close-grained,  and,  though 
very  brittle,  is  exceedingly  durable  when  exposed  to  the 
weather,  and  has  recently  come  into  use  for  interior  finish. 
It  is  not  as  well  suited  for  sills  as  locust. 

Butternut  is  of  a  light  color  and  possesses  a  strongly  marked 
grain.  The  lumber  can  be  secured  only  in  short  lengths,  and 
though  soft  and  easily  worked  it  will  not  split  easily ;  it 
resists  moisture,  and  remains  unaffected  by  heat  until  the 
wood  begins  to  char.  It  is  not  suitable  for  framing  material, 
but  is  used  in  cabinet  work  on  account  of  its  taking  a  very 
high  polish. 

Beech  is  hard  and  tough,  of  a  close,  uniform  texture,  which 
renders  it  desirable  for  tool  handles  and  plane  stocks.  It  is 
used  but  slightly  in  building,  owing  to  its  tendency  to  rot, 
but  may  be  used  where  constantly  submerged. 

Poplar,  or  whitewood,  a  lumber  of  the  tulip  tree,  is  a  large 
straight  forest  tree,  abundant  in  the  United  States.  It  is  light, 
soft,  very  brittle,  and  shrinks  excessively  in  drying.  In  color 
it  varies  from  white  to  pale  yellow.  The  cheapness  and  ease 
of  working  poplar  cause  it  to  be  largely  used  for  the  cheaper 
grades  of  carpentry  and  joinery  work,  but  it  warps  and  twists 
exceedingly  in  even  slight  atmospheric  changes. 

Buttonwood,  also  called  sycamore,  is  the  wood  of  a  tree  gen¬ 
erally  known  as  the  plane  tree.  It  is  heavy,  hard,  of  a  light- 
brown  color,  and  very  brittle.  The  grain  is  fine,  close,  and 
susceptible  of  a  high  polish.  It  is  very  hard  to  vork,  liable 


212 


CARPENTR  Y  AND  JOINER  Y. 


to  decay,  and  has  a  strong  tendency  to  warp  and  twist  under 
variations  of  temperature.  On  this  account  it  is  best  used  for 
veneered  work. 

Apple  and  pear  trees  furnish  wood  to  he  used  for  tool 
handles,  plane  stocks,  and  small  turned  work.  Neither  is 
much  used  in  building.  Pear  wood  is  sometimes  used  for 
carved  panels,  on  account  of  its  yielding  so  easily  to  edge 
tools. 

Boxwood  is  close-grained,  yellow  in  color,  and  on  account 
of  its  lack  of  shrinking  and  warping  tendencies,  very  desir¬ 
able  for  small  carved  and  turned  work.  It  is  particularly 
useful  in  wood  engraving. 

Basswood  is  the  name  given  to  the  American  linden  tree.  In 
general  appearance  it  strongly  resembles  pine,  hut  is  much 
more  flexible.  It  has  a  great  tendency  to  warp,  and  will 
shrink  both  across  and  parallel  to  the  grain.  It  is  much 
used  for  curved  panels. 

Mahogany  is  a  native  tree  of  the  West  Indies  and  Central 
America.  The  color,  grain,  and  hardness  of  the  wood  vary 
considerably  according  to  its  age  and  locality  of  growth.  It 
is  used  for  the  highest  grades  of  joiner  work.  The  straight- 
grained  varieties  do  not  warp  or  shrink  materially  with 
atmospheric  changes,  while  the  cross-grained  varieties  warp 
and  twist  to  a  remarkable  extent,  and  can,  therefore,  be 
used  to  advantage  only  when  veneered  upon  some  more 
reliable  wood.  The  soft  and  inferior  grades  from  Honduras 
and  Mexico  are  called  baywood  to  distinguish  them  from  the 
rich  deep-red  San  Domingo  or  Spanish  mahogany.  Prima  Vera 
or  white  mahogany  is  of  a  creamy  color,  very  much  like  the 
baywood  in  texture,  and  makes  a  beautiful  finish  for  fine  work. 

Rosewood  is  a  heavy,  hard,  and  brittle  wood,  from  several 
trees  native  to  the  tropical  countries.  It  has  a  beautiful 
grain,  alternating  in  dark  brown  and  red  stripings,  which 
when  well  polished  makes  the  surface  one  of  the  handsomest 
products  of  the  vegetable  world.  As  a  veneer,  it  is  applied 
to  all  kinds  of  cabinet,  furniture,  and  joinery  work  where 
richness  and  durability  are  required,  regardless  of  expense. 

Ebony,  a  dark,  almost  jet-black  wood,  native  to  the  East 
Indies  and  parts  of  Africa,  is  heavy,  strong,  and  exceedingly 


QUALITIES  OF  TIMBER. 


213 


hard,  with  an  almost  solid  annual  growth.  It  takes  a  high 
polish,  and  is  used  in  cabinetwork  ;  its  veneers  are  also 
applied  to  interior  work. 

Lignum  vitae  is  an  exceedingly  heavy,  hard,  and  dark- 
colored  wood.  It  is  very  resinous,  difficult  to  split,  and 
soapy  to  the  touch  ;  it  is  used  mostly  lor  small  turned 
articles,  tool  handles,  and  pulley  wheels. 

Sweet-  or  red-gum,  a  tree  of  large  growth,  is  very  plentiful 
in  the  Southern  and  Western  States.  It  is  soft  in  texture, 
but  strong  and  tough,  and  strongly  resembles  light-colored 
walnut.  It  presents  a  very  handsome  appearance  when 
selected  and  well  finished,  but  has  a  tendency  to  warp  and 
shrink,  which  makes  it  unreliable,  unless  used  in  veneered 
work.  It  is  largely  used  for  fine  interior  trim,  and  cabinet¬ 
work. 

Relative  Hardness  of  American  Woods. 

If  the  hardness  of  shell-bark  hickory  is  assumed  to  be  100, 
other  woods  will  compare  with  it  as  follows : 


Shell-bark  hickory 
Pignut  hickory  ... 

White  oak  . 

White  ash  . 

Dogwood . 

Scrub  oak  . 

White  hazel  . 

Red  oak  . 

White  beach . 

Black  walnut . 

Black  birch  . 


100 

Yellow  oak . 

.  60 

.  96 

White  elm  . 

.  58 

.  84 

Hard  maple  . 

.  77 

Red  cedar  . 

.  75 

Wild  cherry  . 

.  73 

Yellow  pine  . — 

.  72 

Chestnut . 

.  69 

Yellow  poplar  . 

.  51 

.  65 

White  birch  . 

.  43 

..  65 

Butternut  . 

.  43 

.  62 

White  pine . 

.  30 

QUALITIES  OF  TIMBER. 

The  best  timber  is  obtained  from  mature  trees,  the  fibers 
of  which  have  become  compact  and  firm,  both  by  the  drying 
up  of  the  sap  and  by  the  compressive  action  of  the  bai  k. 
There  is  a  great  difference  both  in  appearance  and  strength 
between  the  heart-wood,  or  duramen ,  and  the  sap-wood,  or 
alburnum;  in  the  former,  the  fibers  are  firm  and  dense,  and 
possess  a  deep  color ;  in  the  latter,  they  arc  opc  n,  poroiu,  a 
filled  with  sap,  and  are  usually  of  a  pale  color.  The  hea 


214 


CARPENTR  Y  AND  JOINER  Y. 


wood  is  much  stronger,  and  less  liable  to  decay  and  to  the 
attacks  of  insects,  than  sap-wood. 

The  medullary  rays  consist  of  vertical  layers  or  sheets, 
radiating  from  the  center,  and  connecting  the  pith  with 
the  bark,  as  shown  at  i  and,/,  Fig.  1.  They  are  not,  however, 

continuous,  but  are  broken 
by  the  interweaving  of  the 
fibers.  Those  rays  extending 
from  the  pith  to  the  bark  are 
called  primary  rays ;  those 
extending  through  only  a 
portion  of  the  stem  are  called 
secondary  rays.  The  medul¬ 
lary  rays  are  prominent  in 
oak,  beech,  and  sycamore, 
but  are  not  so  well  defined  in  birch,  chestnut,  and  maple. 
It  is  the  presence  of  these  medullary  rays,  sometimes  called 
silver  grain,  that  gives  so  much  beauty  to  quartered  oak. 

Fig.  1  represents  a  section  of  an  oak  or  ash  tree  of  13  years’ 
growth,  the  coarse  texture  formed  of  the  large  sap  vessels 
being  shown  at  a,  the  closer  texture  at  b,  the  bark  at  c,  the 
primary  medullary  rays  at  i,  and  the  secondary  ones  at  j. 

Selecting  the  Stock. — In  good  lumber  for  building  purposes, 
the  heart-wood  should  be  sound  and  mature,  the  sap-wood, 
or  layers  next  the  bark,  being  entirely  removed.  The  wood 
should  appear  uniform  in  texture,  straight  in  fiber,  be  free 
from  large  or  loose  knots,  flaws,  shakes,  or  any  kind  of 
blemish.  When  the  rings  are  close  and  narrow,  they  denote 
a  slowness  of  growth,  and  are  usually  signs  of  strength.  When 
freshly  cut,  the  wood  should  smell  sweet ;  a  disagreeable 
smell  is  a  sign  of  decay.  The  surface,  when  sawed,  should 
not  appear  woolly,  but  be  firm  and  bright,  and  it  should  not 
be  clammy  and  choke  the  saw.  When  planed,  the  wood 
should  have  a  silky  appearance ;  the  shavings  should  come 
off  like  ribbons  and  stand  twisting  around  the  fingers.  When 
the  wood  appears  dull  and  chalky,  and  the  shavings  are 
brittle  and  friable,  it  is  not  first-class  stock.  Good  lumber 
should  be  uniform  in  color ;  when  blotchy  or  discolored  it 
signifies  a  diseased  condition. 


Fig.  1. 


QUALITIES  OF  TIMBER. 


215 


Imperfections. — There  are  various  defects  in  timber  which 
may  he  caused  either  by  the  nature  of  the  soil  in  which  it 
grew  or  by  accidents  due  to  storms,  etc. 

Heart-shakes  are  cracks  or  partings  of  the  fibers,  radiating 
from  the  center  of  the  tree.  They  are  common  in  nearly  all 
classes  of  timber,  and  are  caused  by  the  shrinkage  of  the 
inner  layers  incidental  to  loss  of  vitality ;  the  cracks  are 
wider  towards  the  heart. 

Star-shakes  are  cracks  radiating  from  the  center,  but  differ 
from  heart-shakes  in  that  they  are  wider  towards  the  bark  ; 
they  are  caused  by  the  rapid  drying  of  young  timber  while  it 
is  full  of  sap. 

Cup-shakes  are  curved  splits  which  separate  the  layers,  and 
are  caused  by  severe  wind  storms. 

Rind-galls  are  curved  swellings,  caused  generally  by  resin¬ 
ous  layers  forming  over  a  wound  where  a  branch  has  been 
broken  off. 

Foxiness  is  a  yellow  or  red  coloring,  signifying  the  early 
stages  of  decay. 

Dry-rot  is  a  fungus  growth,  and  can  be  discovered  by  a 
black-and-blue  tinge;  the  end  wood  is  crumbly  and  crisp. 
Timber  thus  affected  is  of  no  permanent  value,  as  the  rot 
continues  until  the  fiber  becomes  powder. 

Twisted  fibers  are  caused  by  the  twist  ing  tendency  of  winds 
blowing  generally  in  one  direction ;  such  timber  possesses 
little  strength,  owing  to  the  oblique  direction  of  the  fibers. 

Knots  are  either  stubs  of  branches  or  the  gnarly  growth 
formed  where  the  branches  are  lopped  off.  Knots  may  be 
small  and  sound,  in  which  condition  they  are  not  objection¬ 
able,  or  they  may  be  large  and  loose  ;  if  large,  the  strength  of 
the  timber  is  very  much  reduced,  and,  if  loose  or  dark  in 
color,  they  will  ultimately  fall  out,  loose  knots  being  the 
stubs  of  dead  branches.  _____ 

QUARTER  AND  BASTARD  SAWING. 

The  term  quarter  sawed  signifies  that  the  log  is  cut  into 
quarters  before  being  reduced  to  boards,  while  the  term 
bastard  sawed  denotes  that  all  the  saw  cuts  are  parallel  to 
the  squared  side  of  the  log.  In  genuine  quarter  sawing  (also 


216 


CARPENTR  Y  AND  JOINER  Y. 


called  rift  sawing)  the  cuts  should  he  as  nearly- as  possible 
at  right  angles  with  the  circles  of  growth,  or  parallel  with 
the  medullary  rays  a,  as  shown  in  Fig.  2 ;  while  in  bastard 
sawing,  the  cuts  are  nearly  parallel  with  the  circles  of  growth 
and  expose  the  edges  of  the  medullary  rays  a  and  the  full- 


Fig.  2. 


Fig.  3. 


face  grain  of  the  laminations,  as  shown  at  b'  and  c'  in  Fig.  3. 
The  advantages  in  quarter  sawing  material  having  well- 
defined  medullary  rays  are  that  it  wears  better,  shrinks  less, 
and  the  silver  grain  presents  a  very  fine  effect. 

Fig.  4  illustrates  four  methods  of  cutting  the  boards  from 

the  “  quarters.”  The  tree  is  first 
quartered  by  cutting  it  on  lines 
ab  and  cd,  after  which  the  quar¬ 
ters  may  be  reduced  to  boards  by 
any  of  the  methods  shown.  The 
best  results  are  secured  by  the 
method  shown  between  a  and  c, 
as  the  saw  cuts  are  nearly  on 
radial  lines,  and  the  full  face  of 
the  silver  grain  will  be  exhibited. 
The  section  between  c  and  b  shows  the  next  best  method ; 
fewer  triangular  strips  are  formed,  but  the  boards  will  not 
present  as  rich  an  effect,  as  many  of  the  medullary  rays  are 


CARPENTR  Y  JOINTS. 


217 


cut  obliquely.  The  result  of  cutting  the  section  between  a 
and  d,  while  economical  in  material,  will  not  give  as  good 
results  as  the  two  former  methods.  Where  thick  material  is 
desired,  the  system  of  cutting  shown  on  the  section  between 
d  and  b  is  adopted,  the  cuts  being  made  in  the  order  in 
which  they  are  marked. 

As  before  stated,  the  best  effects  are  produced  when  the 
saw  cuts  come  parallel,  or  nearly  so,  with  the  medullarj  raj  s , 
this  is  shown  in  Fig.  2.  These  rays  on  the  end  section  are 
marked  a,  and  are  seen  to  cross  the  annual  rings  b  and  c  at 
nearly  right  angles,  so  that  the  edges  of  these  rings  are 
exposed  on  the  face,  and  through  which  the  silver  gram  a' 
emerges.  The  value  of  quarter  sawing  does  not  consist 
merely  in  the  beautiful  figuring  of  the  material,  but  as  it 
places  the  medullary  rays  at  right  angles  with  the  annual 
rings,  it  is  found  that  the  quartered  material  shrinks  less 
than  one-quarter  as  much  in  the  width  as  the  common- 
sawed  stock.  This  is  an  invaluable  virtue,  which  the  joiner 
and  cabinetmaker  are  not  slow  to  appreciate.  Quarter-sawed 
stock  is  also  less  sensitive  to  changes  of  temperature,  and 
when  once  thoroughly  seasoned  and  well  put  together,  it 
makes  an  admirable  finish  both  for  interior  treatment  an* 
furniture,  and  its  beauty  is  greatly  enhanced  with  age. 


CARPENTRY  JOINTS. 


A  bevel-shoulder  joint  (a),  Fig.  5,  is  a  mortise  and  tenon 
used  to  unite  inclined  to  upright  or  horizontal  pieces.  It  is 
made  by  cutting  beveled  shoulders  on  the  inclined  piece  and 
a  corresponding  sinking  in  the  cheeks  of  the  mortise  o  a 

P°  A Zrd^wuth  joint  (5)  is  an  angular  notch  cut  in  a  timber 
to  allow  it  to  fit  snugly  over  the  piece  on  which  it  rests 

A  bridle  joint  (c)  is  one  in  which  the  mortise  is  supplanted 
by  a  tongued  notch  and  the  tenon  by  a  grooved  socket  The 
tongue,  called  the  bridle,  is  equal  to  about  one-third 

thickness  of  the  timber.  .  ,  ... 

A  cogged  joint  {d),  called  also  a  corked  joint,  is  made  wit 


218 


CARPENTR  Y  AND  JOINER  Y. 


Fig.  5.  (a) 


CARPENTR  Y  JOINTS. 


219 


Fig.  5.  [b) 


220 


CARPENTRY  AND  JOINERY. 


a  cog  in  the  top  of  the  lower  timber,  and  a  corresponding 
notch  in  the  under  surface  of  the  upper  timber. 

The  cottered  joint  (e)  is  used  in  tightening  up  tie-beams  to 
king  posts,  etc.,  and  consists  of  a  steel  strap  and  slip  wedges. 

In  a  notched  joint  (/),  made  by  cutting  a  notch  in  each 
piece  of  timber,  the  notches  are  always  less  in  depth  than 
one-half  the  thickness  of  the  material. 

The  dovetail  joint  (g),  used  to  obtain  a  close,  rigid  union, 
consists  of  a  wedged-like  pin  cut  in  the  end  of  one  piece,  and 
a  corresponding  notch  in  the  other. 

A  fished  joint  (h),  used  for  joining  timbers  in  the  direc¬ 
tion  of  their  length,  is  formed  by  butting  the  squared  ends 
together  and  placing  short  pieces  of  wood  or  iron,  sailed  fish¬ 
plates,  over  the  faces  of  the  timbers  and  bolting  or  spiking 
the  whole  firmly  together. 

The  fox-wedged  joint  ( i )  is  used  to  secure  the  tenon  in  a 
mortise  that  is  not  cut  through.  Thin  wedges  of  hard  wood 
are  placed  in  saw  cuts  in  the  end  of  the  tenon.  On  driving 
in  the  tenon  the  wedges  cause  it  to  expand  and  fit  tightly  in 
the  mortise,  which  is  dovetailed  or  widened  out  at  the  back. 

A  halved  joint  ( j )  is  made  by  notching  each  piece  one- 
half  of  its  thickness,  so  that  the  top  and  bottom  surfaces 
of  both  timbers  are  flush.  Beveled  or  dovetailed  halving  is 
shown  at  ( k ). 

The  scarf  joint  ( l )  is  used  where  the  timber  has  to  be 
lengthened  ;  this  joint  forms  a  rigid  splice. 

A  lap  joint  (to)  is  made  by  laying  one  end  of  a  timber  over 
another  and  fastening  them  together  with  bent  straps,  which 
have  screw  ends  by  which  they  may  be  tightened.  The 
efficiency  of  this  joint  can  be  increased  by  inserting  hard¬ 
wood  tongues  across  the  faces  in  contact. 

The  lip  joint  (n)  is  furnished  with  a  lip  a  to  make  a 
stronger  cross-section.  It  may  also  be  applied  to  halved  or 
dovetailed  joints. 

A  tusk-tenon  joint  (o)  is  formed  by  inserting  a  tenon  into  a 
corresponding  mortise.  The  tenon  is  strengthened  by  a 
shoulder  at  the  root  called  a  tusk.  The  tenon  is  generally 
one-sixth  the  thickness  of  the  timber,  and  is  placed  midway 
in  the  depth.  The  upper  shoulder  is  beveled  so  as  to  avoid 


BALLOON  FRAMING. 


221 


cutting  away  the  material  of  beam  into  which  it  is  inserted. 
This  joint  is  a  common  one  for  uniting  tail-beams  to  headers 
in  floor  framing. 

A  checked  joint  (p)  is  made  when  two  pieces  cross  each 
other,  and  it  is  desired  to  reduce  the  height  occupied  by  the 

upper  timber.  „ 

The  socket  joint  (q)  is  formed  by  inserting  the  ends  of  tim¬ 
bers  into  an  iron  casting.  It  is  commonly  used  at  the  apex 
and  toes  of  principal  rafters.  When  used  for  the  latter  pur¬ 
pose,  provision  must  be  made  to  permit  the  evaporation  of 


the  sap.  ,  ,  ...  ,  ,  . 

The  strap  joint,  shown  in  elevation  and  plan  at  (r)  and  (s), 

is  made  by  girding  the  joint  by  a  strong  iron  band.  This 
joint  is  an  approved  method  of  tying  the  foot  of  a  principal 

rafter  to  a  tie-beam  composed  of  two  planks.  .  , 

I  The  tie  joint  (t)  is  one  usually  adopted  to  tie  the  incline 
rafter  to  the  tie-beam,  and  prevent  it  from  spreading. 


BALLOON  FRAMING. 

In  this  system  of  framing,  timbers  of  small  section  are  used 
to  construct  a  light,  skeleton  frame,  whose  rigidity  depends 
entirely  on  its  thin,  canvas-like  covering.  This  is  the  dis 
tinguishing  feature  of  balloon  framing  compared  with  braced 
fraud, m  in  which  the  rigidity  depends  upon  a  well-arranged 

sssssa^ssssx 

points  on  good  construction  wfll  be  noted. 

After  the  wall  a  is  completed, 

,aiVn  a-t1i°hSrr louid  hi 
kept°back  ‘from  L  face  0^1,  .  that  the  outside 

Simple  and  triangles; 

g„:“c  £££  ^  suro 


222 


CARPENTR  Y  AND  JOINER  Y. 


of  the  squares  of  the  other  two  sides.  This  principle  is  illus¬ 
trated  at  the  near  corner  of  the  sill  in  the  figure.  Lines  are 
drawn  on  the  top  of  the  sill  equidistant  from  the  outer  edges, 
and  a  nail  is  driven  at  their  intersection.  From  this  point 
3  ft.  is  measured  on  one  line  and  4  ft.  on  the  other,  and  nails 
are  driven  at  the  points  marked.  Where  the  pieces  are  square 


Fig.  6. 


to  each  other,  the  hypotenuse  will  measure  just  5  ft.  Tri¬ 
angles  with  sides  which  are  multiples  of  3,  4,  and  5,  such  as 
6,  8,  and  10,  9,  12,  and  15,  etc.,  may  he  used  also. 

The  sill  having  been  bedded,  leveled,  and  squared,  the 
cellar  posts  c  are  set  up  on  base  stones,  and  the  beam  d  placed 
in  position ;  the  beam  may  be  attached  to  the  tops  of  the 


BALLOON  FRAMING. 


223 


posts  by  toe-nailing,  but  a  more  workmanlike  method  is  to 
secure  it  by  means  of  iron  drift-pins,  driven  through  the 
beam  from  above  ;  or  by  inserting  dowel-pins  of  wood  or  iron 
in  the  tops  of  the  posts,  and  boring  the  beam  to  suit. 

In  order  to  reduce  the  depth  of  the  wood  liable  to  shrink¬ 
age,  the  top  of  the  beam  is  kept  up  4  in.  higher  than  the 
lower  edge  of  floor  joists  e,  gains,  or  notches  /,  being  cut  out 
of  its  upper  edge,  into  which  seats  the  joists  are  fitted  ;  unless 
this  is  done,  the  joists  will  be  liable  to  split  when  loaded,  as 
indicated  at  1  and  2.  At  the  wall  bearings  g  the  joists  are 
simply  checked  over  the  sill,  but  the  heels  or  bearing  of  the 
joists  on  the  wall  should  be  supported  by  wedging  up  each 
one  with  a  piece  of  slate,  after  the  joist  has  been  spiked  to  the 
sill  and  stud.  The  space  between  the  joists  should  be  filled 
in  with  stone  or  brick  (usually  the  latter)  up  to  the  top  of 
the  joists,  and  7  in.  higher  between  the  studs,  as  at  h ;  this 
prevents  the  passage  ot  air-currents  and  lodgment  for  rats 
and  mice.  To  equalize  the  shrinkage  at  the  bearing  beam 
and  wall  sill,  the  joists  should  rest  on  top  of  the  sill  instead 
of  being  checked  over  it,  as  shown ;  but  in  common  work 
this  is  seldom  done,  as  4  in.  of  effective  height  of  the  stud 
would  thus  be  sacrificed.  In  order  to  provide  for  the  inevi¬ 
table  shrinkage,  the  joists  should  be  kept  about  £  in.  higher  at 
the  center  of  the  building.  When  4"  studs  are  used,  a  firm, 
solid  corner  post  can  be  made  by  nailing  a  2"  X  4"  stud  to 
the  face  of  a  4"  X  6"  scantling. 

The  second  tier  of  joists  should  be  butt-jointed  at  the  cen¬ 
ter  partition  i,  toe-nailed  into  the  plate  j,  and  further  secured 
from  spreading  by  a  fish-plate  well  nailed  to  each  joist. 
Sometimes  the  joists  are  lapped  over  one  another  and  spiked, 
which  gives  each  joist  a  4"  bearing  on  the  partition  ;  but  this 
affects  the  equal  spacing,  and  allows  vibration,  which  may 
crack  the  plaster.  Also,  if  hot-air  pipes  are  to  pass  between 
the  studs,  the  space  thus  contracted  necessitates  a  narrower 
pipe,  with  less  heating  capacity.  The  wall  ribbon  is  shown 
at  k  ;  over  this  ribbon  are  notched  the  joists  l. 

Where  there  are  continuous  partitions,  the  studs  should  be 
toe-nailed  to  the  plate  beneath  and  spiked  to  the  second-floor 
joists.  The  plates  being  lapped  and  spiked  to  the  plate 


224 


CARPENTRY  AND  JOINERY. 


surmounting  the  wall  studs,  tie  the  building  lengthwise,  and 
stiffen  the  partition. 

Before  the  building  is  sheathed,  the  corner  posts  m  should 
be  again  carefully  replumbed  and  adjusted  by  means  of  a 
plumb-bob  suspended  from  the  wall  plate  and  run  down  to  the 
sill,  when  the  most  accurate  adjustment  can  be  made.  The 
sheathing  n  should  be  placed  diagonally  at  an  angle  of  45°,  and 
be  well  nailed  to  each  stud  with  two  or  three  nails,  according 
to  the  width  of  the  board.  The  butt  joints  should  be  cut  on 
the  center  line  of  the  studs.  With  boarding  thus  placed, 
well  fitted  and  nailed,  the  structure  is  completely  braced  in  a 
very  simple  and  effective  manner.  The  outer  surface  should 
be  covered  with  a  layer  of  heavy  building  paper  o,  lapped  at 
the  edges  and  tacked  in  place.  Paper,  being  of  close  texture 
and  a  non-conductor  of  heat,  makes  an  excellent  covering 
material,  rendering  the  building  warmer  in  winter  and 
cooler  in  summer.  The  base  p  should  be  capped  to  throw  off 
the  rain  water,  and  should  project  about  1£  in.  outside  the 
wall.  The  corner  boards,  as  at  q,  1£  in.  thick,  should  be 
firmly  nailed  in  place,  the  inner  edges  being  slightly 
beveled,  so  that  the  siding,  when  sprung  in,  will  fit  tightly. 
The  siding  r  should  be  clear,  white-pine  boards,  beveled  on 
section,  as  shown,  from  f  in.  thick  at  the  lower  edge  to  x%  in. 
at  the  upper  edge,  and  generally  from  4  in.  to  5  in.  wide, 
according  to  the  weathering,  or  exposed  surface.  The  siding 
should  have  a  lap  of  1  in.  or  more,  and  should  be  nailed  at 
each  stud,  the  nails  being  of  sufficient  length  to  pass  through 
the  boarding  and  enter  the  stud ;  this  gives  better  results 
than  if  they  are  simply  driven  into  the  sheathing.  The 
gauge ,  or  exposed  width,  of  the  siding  varies  where  it  comes 
in  contact  with  door  and  window  frames,  in  order  that  the 
horizontal  lines  of  the  siding  will  aline  with  those  of  the  sill 
and  head  of  the  frame.  Great  care  should  be  exercised  in 
fitting  the  siding  in  place ;  when  cut  to  the  required  length 
it  should  be  somewhat  longer  than  the  distance  between 
the  vertical  casings,  in  order  that,  when  sprung  into  position, 
the  end  fibers  will  enter  the  edge  wood  of  the  casings,  and 
thus  insure  a  close  joint,  even  after  the  casings  have  slightly 
shrunk. 


BALLOON  FRAMING. 


225 


Sizes  in  Inches  of  Framing  in  Buildings. 


Balloon-Frame 

Braced-Frame 

u 

Building. 

Building. 

y>p 
•a  ° 

il 

coO 

1 

a> 

S 

Area, 
1,500  Sq. 
Ft.  or 
Less. 

2  Stories 
High. 

Area, 
Dver  1,500 
Sq.  Ft. 

3  Stories 
High. 

Area, 

1,500 

Sq.  Ft. 
or 

Less. 

Area 
Over 
'  1,500 

Sq.  Ft. 

Corner 

posts 

2X4 

2X6 

2X6 

2X6 

10X10 

spiked  to 
4X0 

spiked  to 
6X8 

spiked  to 
4X8 

spiked  to 
6X8 

Sills 

4X8 

4X10 

4X10 

4X10 

6X10 

Plates 

Two  2X4 

Two  2X6 

6X8 

6X10 

6X10 

Interties 

4X8 

6X8 

8X10 

Girts 

Studs, 

1X4 

11X4 

2"  to  3" 

bearing 

3X6 

3X6 

4X6 

plank 

partition 

and 

3X4 

for  parti¬ 
tions. 

opening 

Studs, 
wall  and 

2X4 

2X6 

2X6 

3X6 

partition 

5X8 

6X8 

Braces 

2X4 

2X6 

4X6 

Sheathing 

1X9 

1X9 

1X9 

1X9 

Two  11" 

Rough 

floor 

1X6 

1X6 

1X0 

1X6 

3-41 

Finished 

floor 

1X4 

1X4 

1X4 

1X4 

1-1* 

2X8 

2X  10 

3X8 

3X10 

4X10 

Floor 

to 

to 

to 

to 

joists 

3X10 

3X12 

3X12 

3X12 

10X12 

Rafters 

2X0 

to 

2X8 

2X8 

to 

2X10 

2X8 

to 

2X10 

3X8 

to 

3X10 

4X10 

to 

8X10 

Tie-beam 

3  2X6 

2X8 

2X10 

2X12 

226 


CARPENTRY  AND  JOINERY. 


ROOF  FRAMING. 


LENGTHS  AND  CUTS  OF  RAFTERS. 

The  first  step  is  to  lay  out  a  roof  plan  on  a  board  or  sheet 
of  drawing  paper,  to  a  scale  of,  say,  1£  in.  to  1  ft.  Fig.  7  (a) 
represents  such  a  plan  of  a  roof  of  uniform  pitch,  the  wing 


being  the  same  width  as  the  main  building ;  one  end  of  the 
roof  is  hipped,  while  the  other  ends  are  finished  with  gables, 
as  may  be  readily  understood  by  reference  to  the  perspective 
view  ( b ).  In  both  views,  the  same  letters  refer  to  the  same 
parts. 

Length  and  Cuts  of  Common  Rafters. — At  the  center  of  a  b 
in  (a),  erect  a  perpendicular  cc'  equal  to  the  height  of  the 
ridge  above  the  wall  plates ;  join  c'  and  b ;  then,  the  angle  at 
b  is  the  foot-cut,  and  that  at  e',  the  plumb-cut  of  the  common 


ROOF  FRAMING. 


227 


rafters.  The  length  may  he  found  by  scaling.  The  angles 
are,  transferred  by  means  of  a  bevel  to  the  rafter,  as  shown  in 
(c),  in  which  b  is  the  foot-cut,  and  c  the  plumb-cut. 

Length  and  Cuts  of  Hip  Rafters.— On  the  line  that  represents 
the  hip  on  plan— as  eg  in  (a)— erect  a  perpendicular  ee' 
equal  to  the  height  c  c'  of  the  ridge  ;  join  e'  and  g  ;  the  angles 
at  ef  and  g  are  the  plumb-  and  foot-cuts,  respectively,  and  the 
length  may  be  found  by  scaling.  The  lengths  and  cuts  for 
the  valley  rafter  i  h  are  in  this  case  the  same  as  for  the  hip 
rafter,  and  are  found  in  the  same  way,  as  shown  at  h  and  i' 
in  (a).  Both  hip  and  valley  rafters  have  cheek-cuts,  which 
are  the  same  as  those  of  the  jack-rafters. 

Length  and  Cuts  of  Jack-Rafters. —  Erect  a  perpendicular 
m  e"  at  the  center  of  the  span  /  g ;  with  /  as  a  center,  and 
e'  g,  the  true  length  of  the  hip  rafter,  as  a  radius,  strike  an 
arc  cutting  m  e"  at  e"\  join  /  and  e"',  then  the  angle  at  e"  is 
the  cheek-cut.  The  foot-  and  plumb-cuts  will  be  the  same 
as  for  the  common  rafters.  The  length  of  any  jack-rafter, 
as  o  p,  is  found  by  prolonging  it  to  cut  /  e",  as  at  p';  then 
op',  measured  by  scale,  is  the  length  of  op. 

Cheek-Cut  for  Rafters  of  Any  Pitch.— On  the  face  of  the  rafter 
draw  the  plumb-cut,  as  at  a  b,  Fig.  8 ;  parallel  to  a  b  draw  d  e 


at  a  distance  c  equal  to  the  thickness  of  the  rafter ;  square 
over  from  d  to  /,  and  join  /  and  a,  thus  obtaining  the  cheek- 

cut. 


228 


CARPENTRY  AND  JOINERY. 


fix 

/  i 

i  \ 

i  \ 

i  \ 

/  1 

/  1 

£/  « 

7  l 

i  / 

l  / 

\a 

i 

i 

1  / 

IN 

h  | 

52 

\  l 

X  i 

-iN 

Lengths  of  Hip  or  Valley  Rafters;  Wall  Plates  at  Right  Angles. 

Having  fixed  the  rise  and  run  by  the  square  for  the  common 
rafter,  take  17  in.  for  the  run  of  the  hip  or  valley  rafter. 
Thus,  if  the  roof  is  -one-third,  i.  e.,  8  in.  rise  and  12  in.  run, 
the  hip  or  valley  rafters  will  have  the  same  rise,  8  in.,  and 
17  in.  run.  This  rule  gives  results  too  great  by  about  T6a  in. 
in  10  ft. 

Lengths  of  Jack-Rafters. — Having  obtained  the  lengths  of  the 
first  two  adjacent  jack-rafters  at  the  toe  of  the  hip  rafter,  by 
the  graphic  or  other  method,  measure  the  difference  between 

their  lengths,  and  keep 
adding  this  difference  for 
the  subsequent  ones. 

Miter  Cuts  for  Purlins. 
On  the  squared  end  of 
the  purlin  draw  a  plumb- 
line,  as  at  a  b,  Fig.  9. 
Draw  perpendiculars,  as 
c  and  d,  from  the  corners 
of  the  purlin  to  this  line. 
On  the  upper  edge  of  the 
purlin  lay  off'  a  distance 
d'  equal  to  d,  and  on  the 
lower  edge  lay  off  c' 
equal  to  c ;  from  e  draw 
lines  to  the  points 
marked,  thus  obtaining 
the  lines  for  the  cut. 
This  is  for  a  cut  over  a 
Fig.  10.  hip  rafter ;  where  the 

cut  is  over  a  valley  rafter,  the  bevel  will  be  the  same,  but  d' 
is  laid  off  on  the  lower,  and  d  on  the  upper,  edge. 

Profiling  Hip  and  Jack  Rafters  for  a  Curvilinear  Roof.— In  Fig.  10 
the  arrangement  of  the  rafters  is  shown  in  plan,  e  g  being  a 
hip  rafter,  and  h  l  a  jack-rafter.  In  the  elevation,  b'  c'  is  the 
span  and  oe'  is  the  rise.  To  find  the  shape  of  the  hip 
rafter  eg,  make  e"g"  equal  in  length  to  eg,  and  lay  off 
e"k",  k"  h",  etc.,  equal  to  ek,  kh,  etc.  Erect  perpendiculars 
at  e",  k",  h",  etc.  At  e,  k,  h,  c,  etc.,  drop  perpendiculars 


ROOF  FRAMING. 


229 


cutting  the  curve  e'  g'  at  k',  h',  etc. 
horizontals  cutting  perpen¬ 
diculars  from  e",  k",  h",  etc., 
at  the  points  e"',  h"',  etc.  A 
curve  drawn  through  these 


From  k'  h',  etc.  draw 


points  gives  the  required  out¬ 
line  of  the  hip  rafter.  The 
shape  of  the  jack-rafter  h  l  is 
the  same  as  the  curve  h'  g'. 

PITCHES  FOR  A  GAM¬ 
BREL  ROOF. 

A  method  of  determining 
the  pitches  for  a  gambrel  roof 
is  shown  in  Fig.  11.  The  line 


af  is  made  equal  to  the  width 
of  the  front  plus  the  eave 
projections.  On  the  center 
<7,  with  a  radius  equal  to  one- 
half  of  this  measurement, 
describe  a  semicircle  ahf; 
divide  this  into  five  equal 
parts,  as  at  b,  c,  d,  and  e,  and 
erect  g  h  perpendicular  to  af. 
Draw  ab  and  fe,  the  side 
slopes,  and  b  h  and  e  h,  the 
upper  slopes;  then  abhcf 
will  be  the  outline  of  the  roof. 


A  PLANK  TRUSS- 

Fig.  12  shows  a  trussed 
rafter  suitable  for  a  fiat  pitch 
roof  of  from  30  to  40  ft.  span, 
the  rafters  being  set  at  from 


230 


CARPENTRY  AND  JOINERY. 


21  to  3'  centers.  The  rafters  and  joists  are  2  in.  X  8  inland  of 
a  good  quality  of  spruce  or  hemlock.  The  lattice  braces  are 
1  in.  X  8  in.,  and  are  placed  in  pairs,  one  on  each  side  of  the 
main  members,  to  which  they  are  spiked.  The  spiking  should 
be  well  done,  especially  near  the  supports.  The  tie-member  is 
spliced  at  the  center  of  the  span  by  two  1"  X  8"  fish-plates, 
well  spiked  to  the  ceiling  joist ;  two  iron  dogs,  well  driven 
in,  further  strengthen  the  splice.  The  roof  is  covered  with 
H"  X  6"  tongued-and-grooved  surfaced  spruce,  then  with  a 
layer  of  felt,  upon  which  tin  is  laid.  All  other  necessary 
details  of  construction  are  shown  in  Fig.  12. 


MISCELLANEOUS  NOTES. 


SIDING  A  CIRCULAR  TOWER. 

In  covering  a  circular  tower  with  beveled  siding,  as 
shown  at  (a),  Fig.  13,  it  will  be  found,  on  bending  the  strip 

of  siding  around  the 
cylinder,  that  the  edges 
will  creep  upwards  in 
the  middle,  as  indi¬ 
cated  at  ( b ).  This  if 
owing  to  the  slope  ol 
the  back  of  the  siding, 
next  the  sheathing, 
caused  by  its  lapping 
over  the  upper  edge 
of  the  strip  underneath ; 
so  that  it  really  forms 
part  of  a  conical  sur¬ 
face.  It  will  be  neces¬ 
sary  to  find  the  slope 
length  of  the  cone,  to 
serve  as  a  radius  to 
describe  the  curvature 
to  which  the  lower  edge  of  the  siding  should  be  cut.  Draw  a 
vertical  center  line  a  b  in  (c),  representing  the  center  line  of 


MISCELLANEOUS  NOTES. 


231 


the  tower,  and  at  a  point  b  draw  c  b  and  b  d,  each  equal  to  one- 
half  the  diameter  of  the  tower  on  the  sheathing  line,  plus  the 
thickness  of  the  upper  edge  of  the  siding ;  from  c  or  d  draw  a 
line  towards  a,  having  the  same  inclination  as  the  back  of 
the  siding  on  the  wall ;  the  point  where  the  line  intersects  a  b‘ 
as  at  a,  will  be  tne  vertex  of  the  cone,  and  a  c  will  be  its  slope 
length,  and  also  the  radius  for  describing  the  curve  ced.  As 
the  radius  will  be  too  long  to  lay  down  full  size,  any  chord  of 
the  curve,  as  c  e,  may  be  used,  from  which  offsets  h,  i,  and  j 
may  be  measured  and  laid  down,  so  that  the  points  can  be 
fixed  on  the  floor.  A  few  wire  nails  being  driven  to  mark 
the  points,  a  flexible  strip  run  around  them  will  give  a 
satisfactory  curve,  and  the  lower  edge  of  the  siding  strip 
will  be  cut  as  at  c'  e' d'  in  (d),  the  curve  of  which  is  shown 
greater  than  it  would  be  in  practice,  in  order  to  emphasize 
it.  The  butt  joints  of  the  siding,  as  at  c' d',  being  radial  lines, 
must  be  cut  square  to  the  curve  c'  e' d'. 

Should  special  siding  with  a  straight  back  to  hug  the 
sheathing,  as  shown  at  (e),  be  used,  no  curvature  will  be 
required  for  the  lower  edge,  as,  in  sheathing  a  cylinder, 
boards  with  straight,  parallel  edges  can  be  used. 


PROPORTIONS  OF  ROOMS. 

Church  Dimensions.— In  figuring  the  floor  area  it  is  usual  to 
allow  from  5  to  7  sq.  ft.  for  each  person.  This  includes  space 
occupied  by  passages,  pulpit,  etc.  Width  between  pews, 
back  to  back,  from  30  to  34  in.  Length  of  seat  allowed  for 
adults,  from  18  to  24  in.;  for  children,  from  14  to  16 in.;  height 
of  seat,  18  in.;  width,  from  13  to  15  in. 

Schoolrooms— Width,  from  16  to  24  ft.  Height  of  level 
ceiling,  12  ft. ;  if  floor  area  exceeds  360  sq.  ft.,  13  ft. ;  and  if 
over  600  sq.  ft.,  14  ft.  In  one-story  structures,  where  ceiling 
can  be  raised  to  tie-beams,  the  height  to  wall  plate  may  be 
11  ft.,  and  to  tie-beams  14  ft.  Height  of  window  sills  from 
floor,  4  ft.  Length  allowed  for  seats  of  junior  classes,  from 
14  to  18  in. ;  for  senior  classes,  from  20  to  24  in.  Distance 
apart  for  desks,  back  to  back,  30  in. 


232 


CARPENTRY  AND  JOINERY. 


Acoustic  Proportion  of  Rooms. — Height  2,  width  3,  length 
5  or  6 ;  or  add  height  of  platform  to  height  of  speaker,  and 
half  the  width  of  the  room  for  the  height. 

Stable  Dimensions. — Width  for  building  with  one  row  of 
stalls,  18  ft.,  occupied  as  follows :  Hay  rack,  2  ft.;  length  of 
horse,  8  ft.;  for  harness  hanging  against  wall,  2  ft.;  gutter,  1 
ft.;  and  passageway,  5  ft.  Height  from  floor  to  ceiling,  from 
12  to  16  ft.  Width  of  stalls,  from  5  ft.  9  in.  to  G  ft.  Loose 
boxes  should  he  equal  to  at  least  two  stalls.  Stable  doors,  4 
ft.  wide  X  8  ft.  high.  Coach-house  doors,  from  7  to  8  ft.  wide 
and  10  ft.  high.  Where  practicable  dispense  with  ceiling  and 
place  ventilator  over  each  horse’s  head.  Corn  bins  should  be 
lined  with  galvanized  sheet  iron.  Glazed  brick  make  bright 
and  healthful  walls ;  desirable  tints  are  buff,  cream,  light 
green,  and  French  gray.  Paving  should  be  of  concrete  or 
clinker  brick.  Stalls  should  have  a  fall  of  4  in.  toward  gutter. 
Harness  room  should  be  isolated  from  the  stable,  and  is 
usually  placed  between  the  stable  and  coach  house. 


FLAGPOLES. 

For  a  flagpole  extending  from  30  to  60  ft.  above  the  roof, 
the  following  proportions  give  satisfactory  results  :  The 
diameter  at  the  roof  should  be  made  fa  the  height  above  the 
roof,  and  the  top  diameter  |  the  lower.  To  profile  the  pole, 
divide  the  height  into  quarters;  make  the  diameter  at  the 
first  quarter  £§  of  the  lower  diameter  ;  at  the  second  quarter. 
I ;  and  at  the  third  quarter,  Thus,  if  a  pole  is  41  ft.  8  in. 
high  above  a  roof,  the  lower  diameter  is  fa  of  41  ft.  8  in.,  or 
10  in. ;  that  of  the  first  quarter,  9f  in. ;  the  second,  8£  in. ;  the 
third,  7^  in.  ;  and  the  top,  5  in. 

Flagpoles  may  be  made  of  spruce  or  pine  ;  Oregon  pine 
is  preferable,  and  where  the  entire  sap-wood  is  removed  by 
cutting  the  pole  out  of  the  heart  of  a  large  trunk,  a  durable 
pole  is  obtained.  The  pole  should  be  i>ainted  with  at  least 
four  coats  of  white  lead,  and  should  be  capped  by  a  suitable 
finial,  terminating  in  a  gilded  ball.  Halyards  should  be  at 
least  |  in.  in  diameter,  and  be  of  waterproofed,  braided 
cotton,  or  Italian  hemp. 


MISCELLANEOUS  NOTES. 


233 


PREVENTION  OF  DECAY. 

The  destructive  effect  of  water  in  causing  rot  of  woodwork 
is  well  known,  and  precautions  must  he  taken,  in  the  con¬ 
struction  of  exposed  surfaces,  to  lessen  this  result  as  much  as 
possible.  A  few  of  these  points  are  noted  below. 

The  decay  of  veranda  posts  resting  on  the  floor  is  due  to 
capillary  action ;  every  time  there  is  a  shower  or  the  floor  is 
washed,  some  water  finds  its  way  under  the  post  and  is 
absorbed.  This  can  be  avoided  by  the  interposition  of  an 
iron  shoe,  to  keep  the  post  from  contact  with  the  floor. 

Water  running  down  the  faces  of  projections,  as  window 
sills,  lintels,  etc.,  at  first  drops  off  at  the  lower  angle,  but 
gradually  forms  a  film  across  the  projecting  under  surfaces ; 
the  drops  are  thus  attracted  into  the  stone  or  brick  wall  or 
the  woodwork,  as  the  case  may  be,  causing  disintegration  of 
the  mortar  or  decay  of  the  wood.  A  simple  preventive  for 
this  action  is  to  groove  or  throat  the  under  side,  near  the  edge, 
causing  the  water  to  drip  from  the  line  of  the  groove.  The 
necessity  for  this  exists  where  there  are  horizontal  projections 
exposing  an  under  surface,  such  as  water-tables,  sill  and 
lintel  courses,  copings,  cap  or  drip  members,  and  molded 
bands  or  cornices,  whether  of  wood  or  stone. 

The  lower  sash  of  windows,  unless  properly  constructed 
and  kept  well  painted,  suffers  through  capillary  action.  If  a 
film  of  water  is  allowed  to  form  be¬ 
tween  the  sills  of  the  window 
frame  and  sash,  it  readily  follows 
the  vertical  grain  of  the  stiles ; 
while  the  wind  forces  in  rain 
until  the  inner  sill  is  also  wet. 

This  may  be  prevented  by  form¬ 
ing  grooves  on  the  sill  of  the 
window  frame  and  on  thd  lower 
edge  of  the  sash,  as  shown  in 
Fig.  14. 

Water  absorbed  between  slates  or  shingles  rusts  the  nails 
securing  them,  and  also  rots  shingles.  For  this  reason,  slates 
too  fine  in  texture  are  not  as  good  as  rougher  ones,  as  the 
closer  the  contact  of  the  surfaces,  the  better  does  capillarity 


Fig.  14. 


234 


CARPENTRY  AND  JOINERY. 


act.  Sawed  shingles  are  not  as  good  as  split  ones,  the  woolly 
surfaces  retaining  moisture,  and  being  more  favorable  to  its 
ascent.  Shingled  roofs  should  neither  be  close-boarded  nor 
have  the  shingles  underlaid  with  paper,  in  order  that  the  air 
may  circulate  and  dry  them  more  readily.  Shingles  should 
be  well  dipped  in  creosote  before  being  laid,  and  afterwards 
thoroughly  coated  with  it,  to  render  them  as  impermeable  as 
possible.  Metal-roof  flashings  and  valleys  present  surfaces 
between  which  water  will  creep  up,  and,  unless  they  are 
made  of  sufficient  width  or  height,  the  roof  will  not  be  water¬ 
tight. 


STEEL  SQUARE. 

The  standard  steel  square,  shown  in  Fig.  15,  is  the  one 
known  to  the  trade  as  No.  100,  but  catalogued  by  some  dealers 
as  No.  1,000.  The  square  consists  of  two  parts,  the  blade,  gen¬ 
erally  24  in.  long  and  2  in.  wide,  and  the  tongue,  usually  18  in. 
long  and  1|  in.  wide.  The  outside  edges  on  one  face  are 
divided  into  inches  and  sixteenths,  and  on  the  other  face 
the  inches  are  divided  into  twelfths.  On  the  inside  edge  the 
graduations  are  to  eighth  inches  on  one  side  and  to  thirty- 
seconds  on  the  other. 

On  the  tongue,  near  its  junction  with  the  blade,  Fig.  15  ( b ), 
will  be  seen  a  diagonal  scale  (shown  enlarged  in  Fig.  16), 
used  for  taking  off  hundredths  of  an  inch.  The  line  a  5  is 
here  1  in.  long,  and  is  divided  into  10  parts ;  the  line  c  d  being 
also  divided  into  10  parts,  diagonal  lines  are  drawn  connect¬ 
ing  the  points  of  division  as  shown.  For  example,  to  take 
off  .76  in.,  count  off  seven  spaces  from  c,  eg  equaling  .70  in.; 
now  count  up  the  diagonal  line  until  the  sixth  horizontal 
line  ef  is  reached  ;  then  ef  is  equal  to  .76  in. 

On  the  same  side  of  the  tongue  is  the  brace  scale, 
which  may  be  seen  at  C,  Fig.  15  (5) .  This  scale  gives  the  length 
of  a  brace  of  given  rise  and  run,  or,  in  other  words,  the  length 
of  the  hypotenuse  of  a  right-angled  triangle  with  equal  sides. 
For  instance,  the  hypotenuse  of  a  triangle  each  of  whose 
sides  is  57  in.,  is  80.61  in.  The  length  and  end  cuts  for  a 
brace  of  any  rise  and  run  may  be  found  by  using  the  square 
in  a  similar  manner. 


MISCELLANEOUS  NOTES. 


235 


Go  the  blade,  Fig.  15  (6),  is  shown  the  board-measure  scale, 
the  use  of  which  will  be  explained  by  aid  of  an  example. 
Let  it  be  required  to  find  the  number  of  board  feet  in  a 
V  X  7"  board,  13  ft.  long.  Under  the  12"  mark,  find  the  num¬ 
ber  13,  and  follow  the  horizontal  space  in  which  13  is  found 
to  the  7"  mark ;  the  answer  is  there  found  to  be  7/5  ft.  B.  M. 
If  the  board  is  oyer  1  in.  thick,  the  problem  is  solved  in 


the  same  way,  the  result  being  multiplied  by  the  thickness  in 
inches.  If  the  length  of  the  board  is  greater  than  any  num¬ 
ber  given  under  the  figure  13,  it  should  be  divided  into  parts, 
as  in  the  following  example :  Required  the  contents  i» 
board  measure  of  a  2"  X  9"  plank,  23  ft.  long.  Divide  the 
length  into  two  parts,  10  ft.  and  13  ft.;  the  contents  of  the  10' 


236 


CARPENTRY  AND  JOINERY. 


part  is  found,  as  before  shown,  to  be  7f^  ft.  B.  M.;  that  of  the 
13'  board  to  be  9T%  ft.  B.  M.  Therefore  the  total  contents 
(if  1  in.  thick)  is  -f  9T92  =  17T32  ft.  B.  M.;  but  as  the  board 
is  2  in.  thick,  the  contents  are  2  X  17^,  or  34£  ft.  B.  M. 

The  octagonal  scale,  found  on  the  tongue  at  A  B,  Fig.  15 

(a),  is  used  in  inscribing  an  octa¬ 
gon  in  a  square.  The  scale  is 
marked  10,  20, 30,  etc.  To  inscribe  an 
octagon  in  a  12"  square  (see  Fig.  17), 
b  draw  the  lines  a  b  and  c  d,  bisecting 
the  sides;  from  d  markde  and  d/, 
each  equal  to  12  divisions  on  the 
octagonal  scale;  mark  bg,  etc.,  in 
the  same  way,  and  draw  eg,  a  side 
of  the  required  octagon.  The  other 
sides  may  be  similarly  found.  For  a 
10"  square,  make  d  e  equal  to  10  divisions ;  for  a  7"  square, 
equal  to  7  divisions,  etc. 

In  Fig.  18  (a)  is  shown  an  adjustable  fence,  a  strip  of  hard 


Fig.  18. 


wood  about  2  in.  wide,  1£  in.  thick,  and  2ls  ft.  long.  A  saw 
kerf,  into  which  the  square  will  slide,  is  cut  from  both  ends, 
leaving  about  8  in.  of  solid  wood  near  the  middle.  The  tool 
is  clamped  to  the  square  by  means  of  screws  at  convenient 
points,  as  shown.  Let  it  be  required  to  lay  out  a  rafter  of  8' 


JOINER  Y. 


237 


rise  and  12'  run.  Set  the  fence  at  the  8"  mark  on  the  blade, 
and  at  the  12"  mark  on  the  tongue,  clamping  it  to  the  square 
with  li"  screws.  Applying  the  square  and  fence  at  the  upper 
end  of  the  rafter,  we  get  the  plumb-cut  d  e  at  once.  By  apply¬ 
ing  the  square,  as  shown,  twelve  times  successively,  the 
required  length  of  the  rafter  and  the  foot-cut  c  b  are  obtained. 
In  this  case  the  twelve  applications  of  the  square  are  made 
between  the  points  c  and  d.  Bun  and  rise  must  also  be  meas¬ 
ured  between  these  points.  If  run  is  measured  from  the  point 
b,  which  will  be  the  outer  edge  of  the  wall  plate,  it  will  be 
necessary  to  run  a  gauge  line  through  b  parallel  to  the  edge  of 
the  rafter,  and  subtract  a  distance  eg  from  the  height  of  the 
ridge,  to  give  us  the  correct  rise.  The  square  must  then  be 
applied  to  the  line  b  g.  A  rafter  of  any  desired  rise  and  run 
may  be  laid  off  in  this  manner  by  selecting  proportional  parts 
of  the  rise  and  run  for  the  blade  and  tongue  of  the  square. 
For  a  half-pitch  roof,  use  12  in.  on  both  tongue  and  blade ; 
for  a  quarter-pitch,  use  6  in.  and  12  in.;  for  a  third-pitch  use 
8  in.  and  12  in.,  etc.  The  terms  half-pitch,  quarter-pitch, 
etc.,  refer  to  the  height  of  the  ridge  expressed  as  a  fraction  of 
the  span. 

JOINERY. 


JOINTS  IN  JOINERY. 

A  beaded  joint  (a)  Fig.  19,  is  one  disguised  by  a  quirked 
bead  which  is  worked  on  one  edge ;  this  joint  is  used  in 
matched  lining,  etc. 

Butt  joints  ( b ),  (c),  and  (d),  are  used  for  returns,  when  one 
piece  is  fitted  to  the  edge  of  anothei’,  and  may  be  rebated, 
matched,  or  plain-butted,  as  required. 

The  feathered  or  slip-tongue  joint  (e),  formed  by  plowing 
correspoixding  grooves  in  adjacent  pieces  and  filling  it  with  a 
slip  tongue,  is  generally  employed  for  plank  flooring. 

A  grooved,  tongued-and-mitered  joint  (/)  possesses  the  quali¬ 
ties  of  strength  and  effectiveness,  and  no  edge  grain  is  exposed. 

The  half-lap  dovetail  joint  ( g )  is  a  form  in  which  the  dove¬ 
tails  appear  only  on  one  side,  and  is  the  method  adopted  for 
drawer  fronts. 

P 


238 


CARPENTRY  AND  JOINERY. 


Fig.  19. 


JOINERY. 


239 


The  lapped-and-tongucd  miter  joint  ( h )  is  somewhat  similar 
to  (/),  but  a  slip  tongue  is  inserted  instead  of  being  worked 
out  of  the  solid  material. 

A  lapped  miter  joint  (i)  is  made  by  rebating  and  mitering 
the  boards  to  be  joined,  and  securing  them  with  nails. 

A  miter-and-butt  joint  (j)  is  a  good  form  for  an  angle  joint 
and  is  simpler  than  ( i ). 

A  miter-keyed  joint  is  a  miter  strengthened  by  a  slip  feather, 
as  at  ( k ),  or  with  slips  of  hard  wood  fitted  into  saw  kerfs, 
as  at  (0- 

A  rabbeted  joint  (m)  is  formed  by  cutting  rectangular  slips 
out  of  the  edges  of  the  boards  to  a  depth  generally  equal  to 
one-half  of  their  thickness,  the  tongues  thus  formed  being 
lapped  over  each  other. 

A  rule  joint  ( n )  is  a  hinged  joint  used  for  the  leaves  of 
tables,  etc. 

Beveled  joints  ( o )  and  (p)  are  formed  to  close  tightly  and 
exclude  the  wind  and  water. 

The  blind  dovetail  joint  (q),  used  for  boxes  and  cabinets 
where  the  dovetails  are  not  to  show,  is  made  by  dovetailing 
three-fourths  of  the  thickness  of  the  board  and  mitering  the 
other  fourth. 


DOORS. 

Proportions.— The  ratio  between  the  width  and  height  of 
doors  at  main  entrances  and  in  public  buildings  is  usually  as 

1  to  2 ;  that  is,  the  height  is  twice  the  width.  For  single 
doors  in  dwellings  and  offices,  the  ratio  should  be  as  1  to  2\ ; 
or  the  height  should  be  ‘2k  times  the  width  ;  doors  2'  8"  X  6'  8" 
and  8'  X  7'  6",  are  thus  proportioned. 

The  width  of  a  door  is  regulated  by  the  purpose  for  which 
it  is  intended  ;  in  public  buildings  provision  is  made  for  the 
passage  of  several  persons  at  a  time,  while  in  private  houses 
and  offices  a  width  suitable  for  one  person  is  sufficient.  In 
the  former  case,  the  width  may  be  from  6  to  14  ft.,  while  in 
the  latter,  the  general  rnle  makes  the  minimum  width 

2  ft.  8  in.  for  communicating  doors,  and  2  ft.  for  closet  doors. 
A  hinged  door  more  than  4  ft.  wide  should  be  made  double ; 
that  is,  in  two  folds.  As  double  folding  doors  take  up  much 


240 


CARPENTRY  AND  JOINERY. 


wall  space  when  kept  open,  sliding  doors  are  frequently  sub¬ 
stituted.  Where  there  are  several  doors  of  different  widths  in 
the  same  room,  to  give  a  better  effect  to  the  interior  treat¬ 
ment  the  height  of  the  principal  doors  should  be  fixed  by  the 
proportion  given,  and  the  others  made  the  same  height.  If 
the  width  of  double  or  sliding  doors  does  not  exceed  6  ft.,  the 
height  may  be  that  of  principal  doors,  but  if  wider,  the  height 
should  he  one-fourth  more  than  the  width.  The  width  of 
sliding  doors,  however,  is  largely  regulated  by  the  depth 
obtainable  for  the  pocket  in  the  partition. 

Framing. — The  width  of  the  stiles  and  top  rail  should  be 
about  one-seventh  the  width  of  the  door,  the  bottom  rail 
about  one-tenth  the  height,  and  the  muntins  and  lock-rails 
£  in.  less  in  width  than  the  stiles.  The  thickness  will  depend 
somewhat  on  the  style  of  finish  and  the  class  of  lock  to  be 
used.  If  the  door  framing  is  solid  and  rim  locks  are  used,  the 

thickness  for  chamber  doors  may  be 
1\  in.;  if  mortise  locks  are  used,  the 
thickness  should  not  be  less  than  1£ 
in.  Solid  doors  for  principal  rooms 
are  made  from  1£  in.  to  2  in.,  and 
entrance  and  vestibule  doors  from 
2£  in.  to  2£  in.  thick.  When  doors 
are  veneered,  the  thickness  is  usu¬ 
ally  increased  £  in. 

When  mortise  locks  are  used,  the 
doors  should,  for  strength,  be  framed 
with  a  lock-panel  so  that  the  joints 
adjacent  to  the  lock  will  not  be 
injured. 

Construction. — The  mode  of  con¬ 
structing  a  5-paneled  door  is  shown 
in  Fig.  20,  certain  parts  being  re¬ 
moved  to  clearly  show  the  joints. 
The  parts  marked  a  are  the  outer 
stiles ;  b,  the  muntins ;  c,  the  bottom 
rail ;  d,  the  lock-rails ;  e,  the  top  rail ;  /,  the  lower  panels ;  g, 
the  lock-panel,  and  h,  the  upper  panels.  The  mortises  i  are 
made  one-third  the  Ihickness  of  the  framing  into,  which  the 


JOINERY. 


241 


tenons  j  are  fitted.  The  edges  of  the  framing  are  grooved  i  in. 
deep,  to  receive  the  panels,  the  width  of  the  groove  being  the 
same  as  the  thickness  of  the  tenon.  The  upper  edge  of  the 
tenons  of  the  top  rail  and  the  lower  edge  of  the  tenons  of 
the  bottom  rail  are  haunched,  as  shown  at  k.  The  bottom  rail 
has  double  tenons  with  a  bridge  between  the  mortises.  The 
muntins  are  mortised  into  the  rails.  The  panels  should  be 
kept  from  }  to  T3^  in.  less  than  the  width  of  the  space  between 
grooves,  to  permit  expansion. 

In  putting  the  door  together,  only  the  shoulder,  or  that 
portion  of  the  tenon  next  the  panel,  should  be  glued,  so  that 
in  case  of  shrinkage  or  swelling  the  joints  will  remain  close. 
When  the  stiles  are  driven  up  and  the  clamps  applied,  the 
wedges  l  should  be  well  fitted,  should  have  the  edges  next  the 
tenons  brushed  with  glue,  and  be  driven  tightly  in.  The 
horns  m,  or  extra  lengths  of  the  stiles  during  construction, 
are  designed  to  withstand  the  pressure  exerted  when  the  end 
wedges  are  driven  in,  which  would  otherwise  be  forced  out  by 
shearing  the  fibers  of  the  wood  beyond  the  mortise,  thus 
destroying  the  joint. 

Fitting. — The  width  of  the  door  should  be  about  T35  in.  less 
than  the  width  between  the  jambs,  allowing  a  clearance  of 
about  332  in.  on  each  side,  and  the  opening  edge  should  be 
slightly  beveled.  The  standard  bevel  to  which  locks  are 
made  is  }  in.  in  2|  in.,  but  where  the  door  is  narrow,  it  may 
require  the  lock-face  beveled  to  as  much  as  £  in.  in  2  in.,  or 
even  more.  An  equal  clearance  should  be  left  at  the  upper 
rail,  while  the  bottom  rail  may  require  from  |  in.  to  i  in.,  in 
order  that  the  door  may  swing  clear  of  the  floor  covering. 
Where  “saddles”  are  used — which  are  not  to  be  recom¬ 
mended — the  door  may  fit  within  335  in.  An  appreciable 
amount  of  the  clearance  will  be  taken  up  by  the  layers  of 
paint  or  varnish. 

Butts. — A  simple  rule  for  finding  the  width  of  butt  required 
for  any  door  is :  To  twice  the  thickness  of  the  door,  less  £  in.,  add 
the  greatest  amount  of  projection  of  any  part  of  the  door  casing 
beyond  the  face  line  of  the  door  ( which  is  usually  the  base  block). 
Thus,  if  a  door  is  2  in.  thick,  and  the  base  block  projects  15 
in.,  the  width  of  the  butt  will  be  2  in.  +  2  in.  5  in.  +  1  j  in., 


242 


CARPENTRY  AND  JOINERY. 


or  5f  in.,  in  which  case  a  b\"  width  would  be  used.  The 
edge  of  the  butt  will  thus  be  kept  |  in.  back  from  the  face  of 
the  door.  One-half  of  the  thickness  of  the  butt  should  be  out 
out  of  the  door,  and  one-half  out  of  the  jamb  of  the  frame.  In 
locating  the  butts,  it  is  usual  to  keep  the  lower  end  of  the 
lower  butt  in  line  with  the  upper  edge  of  the  lower  rail, 
while  the  top  end  of  the  upper  butt  may  be  kept  from  6  to  7 
in.  below  the  upper  edge  of  the  top  rail.  Where  three  butts 
are  used,  it  is  well  to  keep  the  lower  end  of  the  intermediate 
butt  in  line  with  the  upper  edge  of  the  lock-rail,  instead  of 
placing  the  butt  midway  between  the  upper  and  lower  butts, 
as  the  butts  will  then  line  up  with  the  framing.  By  keeping 
the  pin  of  the  lower  butt  slightly  in  advance  of  the  upper 
butt,  the  door,  in  opening,  will  rise  at  the  toe  and  increase 
the  clearance,  so  that  inequalities  in  the  floor  level  may  be 
overcome.  For  first-class  working  doors  the  following  con¬ 
ditions  must  be  observed :  first ,  the  floor  must  be  level  in 
every  direction ;  second ,  both  jambs  of  the  door  frame  must 
be  accurately  plumbed,  facewise  and  edgewise,  else  the  toe  of 
the  door  will  either  rise  above  or  fall  towards  the  floor  when 
operated ;  third ,  the  head-jamb,  or  transom,  as  the  case  may 
be,  must  be  level ;  fourth ,  the  butts  must  be  of  good  quality, 
well  fitted,  and  the  pins  kept  true  to  line. 


,  WINDOWS. 

Area.— The  following  proportions  are  given  by  different 
authorities  for  fixing  the  amount  of  window  surface  :  (1)  One- 
eighth  of  the  wall  surface  should  be  windows.  (2)  The  area 
of  glass  should  equal  at  least  ^  of  floor  area.  (3)  One  square 
foot  of  glass  should  be  allowed  to  100  cu.  ft.  of  interior  space 
to  be  lighted.  It  is  better  to  have  a  surplus  than  a  deficiency 
of  light,  as  if  too  bright,  it  can  be  regulated  by  blinds  or 
shades. 

Design. — The  height  of  the  window  should  be  twice  its 
Width.  Architraves  should  be  from  £  to  }  the  width  of 
the  window  opening,  and  where  pilasters  adjoin  architraves 
their  width  should  equal  that  of  the  latter.  Where  consoles 
are  used  their  length  should  not  be  less  than  |  nor  greater 
than  \  the  width  of  the  opening.  The  entablature  should 


JOINERY. 


243 


oe  from  i  to  ^  the  height  of  the  opening.  Where  engaged 
columns  flank  windows,  at  least  f  of  the  column  should  pro¬ 
ject  beyond  the  face  of  wall. 

To  obtain  a  uniform  frieze  line  around  rooms  in  dwell¬ 
ings,  it  is  well  to  keep  the  window  and  door  heads  equi¬ 
distant  from  the  ceiling.  Thus,  where  the  walls  are  10  or  10i 
ft.  high,  and  the  doors  8  ft.  high,  the  top  of  the  casing  is  from 
18  to  24  in.  from  the  ceiling.  This  space  may  he  occupied  by 
frieze  and  cornice,  or  a  picture  mold  may  extend  around  the 
room  in  line  with  the  upper  edge  of  the  door  and  window 
casings.  Where  ceilings  are  not  over  14  ft.  high,  this  same 
effect  can  be  obtained  by  introducing  transom  sash  over  the 
doors,  filling  these  with  either  chipped  plate  or  art  glass. 

The  glass  line  of  windows  in  dwellings  should  be  about 
30  in.  from  the  floor  for  principal  rooms,  and  about  36  in.  for 
bedrooms.  In  all  cases,  the  heads  of  windows  should  be  as 
near  the  ceiling  as  the  construction  and  interior  scheme  of 
treatment  will  permit,  to  obtain  better  light  and  ventilation. 
The  meeting  rails  of  window  sash  should  be  placed  not 
less  than  5  ft.  9  in.  above  the  floor ;  otherwise,  the  rail  will  be 
on  a  level  with  the  eyes,  obstructing  the  view  and  detract¬ 
ing  from  the  effect  of  the  window.  On  this  account  the 
height  of  the  upper  sash  is  sometimes  made  only  i  that  of  the 
lower,  or  j  the  clear  height.  For  buildings  of  any  preten¬ 
sions,  it  is  a  mistake  to  cut  up  the  sash  into  small  panes.  It 
should  be  remembered  that  windows  are  designed  for  the 
purpose  of  lighting,  and  all  obstructions  created  by  sash  bars 
detract  from  the  desired  result.  Where  the  designer  prefers 
to  have  window  sash  subdivided,  metallic  bars  of  zinc,  copper 
or  lead  will  be  found  more  durable  than  wood,  and  will  not 
take  up  so  much  of  the  daylight  area. 

Sashes  should  slide  vertically,  counterbalanced  by  means  of 
cord,  chain,  and  weights,  or  by  spring  sash  balances  Those 
that  are  hinged  and  open  inwards  cannot  be  made  water-tight, 
and  those  opening  outwards  are  likely  to  be  injured  by  e 
action  of  wind,  so  that  for  general  service  the  best  results 
are  obtained  by  use  of  sliding  sash.  Sash  stops  should  be 
fastened  with  screws  passing  through  slotted  sockets,  thus 
preventing  the  sashes  from  rattling  and  v  arping. 


244: 


CARPENTRY  AND  JOINERY. 


Construction.— In  Fig.  21  is  shown  a  view  of  a  window 
frame  with  sliding  sash,  adapted  for  a  frame  building.  The 
pulley  stile  a  may  be  from  If-  to  If  in.  thick,  and  should 


he  tongued  into  the  blind 
stop  b  and  the  plaster  cas¬ 
ing  c,  each  of  which  is  \  in. 
thick.  These  tongues 
make  the  stiles  rigid,  pre¬ 
venting  them  from  deflect¬ 
ing  sidewise  when  the 
sashes  are  being  operated. 
An  open  space  of  from  2  to 
2£  in.  is  left  between  the 
back  of  the  pulley  stile  and 
the  rough  stud,  thus  form¬ 
ing  a  box  for  the  weights. 
A  movable  pocket  for  the 
insertion  of  the  weights  is 
cut  out  of  the  lower  portion 
of  each  pulley  stile  on  the 


inside ,  so  that  it  may  be  covered  by  the  lower  sash.  The 
parting  strip  d  is  f  or  f  in.  thick,  and  passes  into  a  groove 
f  in.  deep  in  the  pulley  stile.  The  outside  casing  e,  If  in. 
thick  X  5  in.  w'ide,  is  firmly  nailed  through  the  blind  stop 
into  the  pulley  stile  and  to  the  wall  sheathing.  The  inner 
face  of  the  window  frame  is  finished  with  a  casing,  which 
may  be  of  any  style  of  finish — in  this  case,  by  an  architrave, 
the  width  being  sufficient  to  cover  the  plaster  joint.  The  sash 
stop  g,  from  f  to  f  in.  thick,  is  secured  with  round-headed 
screws  passing  through  slotted  sockets  for  adjustment.  The 
members  g,  d,  and  b  should  be  kept  in  line,  their  projection 
beyond  the  face  of  the  pulley  stile  being  regulated  by  the 
thickness  of  the  sash  stop. 

The  sill  h,  from  If  to  If  in.  thick,  is  tongued  into  the  pul¬ 
ley  stiles  and  well  nailed.  Sills  are  sometimes  made  with  a 
straight  inclined  surface  instead  of  being  worked  with  two 
facias,  as  shown.  When  water  collects  on  the  sill,  it  is  readily 
drawn  under  n,  the  lower  rail  of  the  sash,  by  capillarity,  or 
driven  in  by  wind ;  by  raising  the  surface  under  the  sash 


JOINERY. 


245 


above  the  level  of  the  outer  portion,  and  running  a  small 
rounded  groove  in  the  fillet,  the  effect  of  the  wind  is  to  divert 
the  water  outwards.  Under  h  is  placed  the  subsill  i,  It  in. 
thick  which  is  attached  to  the  pulley  stile,  and  likewise 
grooved  for  the  reception  of  the  beveled  siding  j.  For  dur¬ 
able  work,  the  window  frames  should  be  put  together  with 
stiff  white-lead  paint,  particularly  adjacent  to  the  sill  and 
subsill.  The  sashes  k  are  made  from  If  to  If  in.  thick. 
Strength  is  added  to  the  upper  sash  by  the  elongation  of  the 
stile  forming  a  molded  horn,  as  by  this  device  the  tenon  of 
the  meeting  rail  m  can  be  made  equal  to  its  thickness.  The 
meeting  rails,  If  to  If  in.  thick,  according  to  width  of  open¬ 
in'*  may  be  double-  or  single-beveled,  as  shown,  so  that  they 
will  come  tightly  together  when  closed.  The  lower  rail  n 
may  be  from  3  to  4|  in.  wide,  and  should  be  accurately  fitted 
to  the  sill ;  the  outer  edge  should  be  clear  about  |  in.,  but  the 
inner  portion  should  be  in  contact  with  it,  thus  preventing 
the  ready  passage  of  water.  The  inner  face  should  be  rehated 
and  beveled  to  fit  the  edge  of  the  stool  o.  11ns  stool  should 
be  rebated  to  form  an  air-tight  joint,  and  be  bedded  m  white 
lead  An  apron  p  is  fixed  to  the  edge  of  the  sill  and  to  a 
Blaster  ground  q,  and  finished  with  a  bed  mold  as  shown. 
The  length  of  the  apron  should  be  equal  to  the  width  from 
out  to  out  of  casings,  and  have  the  moldings  returned  on 

^^n  Fig.  22  is  shown  a  box-frame  window,  suitable  for  a 
stone  orVick  wall.  The  general  design  and  construction 
of  the  frame  and  sash  are  similar  to  that  shown  in  F>g.  21  the 
milv  changes  being  in  parts  that  require  to  be  adapted  to 
a  new  condition.  In  brick  walls  it  is  usual  to  set  the  window 
frames  during  the  erection  of  the  walls,  thus  facilitating  the 
plumbing  of  the  brick  jambs,  particular  care  being  taken  o 
bmce  the  frames,  in  order  to  keep  them  plumb  and  level. 
By  keeping  the  blind-stop  casing  a  1  m.  wider  than  the  back 
lining  the  frame  can  be  firmly  held  in  place  after  the 
braces  have  been  removed.  The  sill  c,  made  of  3"  plank,  is 
(or  should  be)  bedded  in  haired  lime  mortar,  or  for  first-class 
work  stiff  white-lead  paint  and  white  sand.  The  groove  on 
the  bed  permits  the  formation  of  a  mortar  tongue,  making  it 


246 


CARPENTRY  AND  JOINERY. 


practically  air-tight ;  the  slightest  shrinking  and  warping  of 
the  sill  allows  the  passage  of  air  and  water,  unless  this  device 

is  adopted.  A 
finished  casing  d 
may  be  attached 
to  the  inner  frame 
casing  e ,  after  the 
building  is  ready 
for  trimming, 
thus  covering  its 
marred  condi¬ 
tion.  The  win¬ 
dow  stool  or  seat 
f  rests  on  furring 
strips,  and  is 
tongued  into  the 
sill,  providing  for 
its  expansion  and 
contraction ;  it  is 
generallyfinished 
with  a  molded 
apron  g.  The 
jamb  lining  h  is  tongued  into  the  finished  casing,  and  the 
opening  trimmed  with  a  casing,  such  as  i,  nailed  to  the 
lining  h  and  the  rabbeted  plaster  ground./. 

The  hanging  stile  k  in  brick-set  frames  is  attached  thereto 
before  setting,  but  where  outside  blinds  are  not  used,  an 
angle  mold  may  be  substituted. 

In  stone  walls,  window  frames  are  not  usually  set  until  the 
building  is  roofed  and  either  prepared  for  the  plastering,  or 
when  the  plastering  has  been  completed.  There  are  two 
reasons  for  this,  the  principal  one  being  the  difficulty 
experienced  in  setting  jamb  stones  and  lintels  while  the 
frame  is  in  position,  and  the  second  that,  with  all  due  care, 
the  frames  are  more  or  less  damaged  during  building  opera¬ 
tions  and  are  never  so  true  to  line,  level,  and  plumb  as  those 
set  in  place  after  the  walls  are  completed.  When  set  in  this 
latter  order,  it  is  necessary  to  encase  the  masonry  openings 
with  screeds  or  wooden  strips,  carefully  alined  and  plumbed, 


JOINERY. 


247 


and  so  arranged  to  allow  for  a  bed  of  haired  mortar  iin. 
thick  around  the  jambs  and  window  head.  The  frames  are 
secured  by  means  of  holdfasts  or  wall  plugs.  When  set  In 
this  manner,  the  casing  d  is  not  required,  unless  it  be  that 
the  interior  trim  is  of  a  material  different  from  that  of  the 
window  frame. 


NOTES  ON  STAIRWAYS. 

Proportioning  Treads  and  Risers. — 1.  Take  the  sum  of  two 

risers  and  subtract  it  from  2U  inches  ;  the  result  will  be  the  width 
of  the  tread.  This  rule  is  based  on  the  assumption  that  an 
average  step  is  2  ft.  and  that  the  labor  of  lifting  the  foot  verti¬ 
cally  is  twice  that  exerted  in  moving  Treads.  Risers, 
horizontally,  consequently  the  width  Inches.  Inches. 


of  the  tread,  added  to  twice  the  height  6  8£ 

of  the  riser,  should  be  equal  to  2  ft.  7  8 

2.  The  first  column  of  the  accom-  8  7£ 

panying  table  gives  the  width  of  treads ;  9  7 

the  other  gives  the  corresponding  height  10 

of  risers.  11  6 

3.  The  product  of  the  tread  and  risers  12  5? 


should  equal  66  inches:  thus, 
with  a  tread  of  11  in.  the 
riser  would  be  6  in.;  with  a 
riser  of  7  in.,  the  tread 
would  be  9f  in. 

Miter  Bevel  for  Stringer 
Cut.— The  following 
method  is  of  service  in  ob¬ 
taining  the  accurate  bevel 
to  apply  on  the  edge  of  a 
stair  stringer,  where  it  is 
desired  that  the  riser  miter 
with  the  stringer,  as  in  an 
open  string  stairway.  By 
the  use  of  the  pitch  board, 
mark  on  the  outside  face 
of  the  stringer  the  cuts  for 
the  treads  and  risers,  as  in  Fig.  23.  Draw  be  parallel  to  ad. 


248 


CARPENTRY  AND  JOINERY. 


and  at  a  distance  t  from  ad  equal  to  the  thickness  of  the 
stringer.  At  b,  draw  be  square  across  the  upper  edge  of 
the  stringer,  and  connect  c  and  a.  Then  bac  is  the  miter 
bevel  required.  At  a'  is  shown  a  bevel  set  to  the  line 
obtained,  so  that  it  can  be  used  at  all  the  other  riser  lines. 


DEVELOPMENT  OF  A  RAKING  MOLD. 

In  Fig.  24  is  shown  a  method  for  determining  the  cross- 
section  of  a  raking  mold  to  miter  with  a  given  eave  mold. 

This  method  will  apply 
equally  well  to  any  mold¬ 
ing.  The  eave  mold  in  this 
case  is  a  cyma  recta,  the 
profile  being  shown  as 
abfhjc.  Divide  the  out¬ 
line  into  any  number  of 
equal  parts,  as  at/,  h,  j,  etc. 
Draw  any  horizontal  line 
Ik  and  erect  perpendicu¬ 
lars  from  /,  h,j,  etc.,  cut¬ 
ting  the  line  Ik.  Draw 
a  l"  at  the  required  angle 
and  draw  be,  fg,  etc.,  parallel  to  a l".  From  any  point  l', 
lay  off  the  distance  l'  kf  and  subdivisions  equal  to  l  k.  Drop 
perpendiculars  to  al’’  from  V,  k',  etc.  intersecting  be,  fg, 
etc.  Through  the  intersections  thus  found,  trace  the  curve 
V  c',  which  is  the  profile  of  the  required  mold. 

To  find  the  profile  of  a  vertical  cut  in  the  raking  mold,  at 
any  point,  as  l",  lay  off  l"  k"  and  subdivisions  parallel  to  l  k. 
Proceed  to  find  points  e,  g,  i,  c" ,  etc.,  as  before. 


HOPPER  BEVELS. 

In  making  hoppers  or  boxes  with  inclined  sides,  it  is 
necessary  to  obtain  the  face  and  edge  bevels ;  when  the  sides 
are  mitered,  the  edge  bevel  is  called  the  miter  bevel,  and 
when  they  are  butted,  it  is  termed  the  butt  bevel.  In  Fig.  25 
the  diagrams  are  assumed  to  be  laid  out  on  a  board,  as  if  in 
bench  practice. 


JOINERY. 


249 


In  (a),  let  c  b  be  the  width  of  a  side  of  the  hopper,  and  ce 
the  splay  ;  let  c  be  on  the  edge  k  l.  Strike  the  arc  pj,  and 
draw  cj  square  to  k  l ;  then  cj  is  the  width  of  the  stuff.  Lay 
out  the  thickness  b  a ;  draw  a  d  parallel  to  c  b  ;  also,  c  d 
parallel  to  b a ;  and  cbad  will  represent  a  section  of  the 


W 

Fig.  25. 

board.  Project  b  to  b',  and  draw  cb then  the  angle  gb'c 
will  be  the  face  bevel.  Make  h  h’  equal  to  b  a,  and  draw  g '  h'; 
project  a  to  a';  and  draw  b'a',  then  g b'a'  will  be  the  miter 
bevel.  If  the  edges  are  cut  off  along  the  line  f  a,  the  miter 
bevel  will  be  45°. 

If  the  hopper  is  to  have  butt  joints,  the  face  bevel  is  found 
as  above  shown.  To  obtain  the  butt  bevel,  proceed  as 
follows  :  Draw  a f  through  a,  parallel  to  g  h  ;  project  /  to  /  on 
g'  h',  and  draw  b'f ;  then  the  angle  g  b'f  will  be  the  butt  bevel. 

In  (b)  is  shown  a  perspective  view  of  the  board  kg  hi, 
with  the  bevels  in  position,  gb'c  and  g  b'  a '  being  those 
required  for  a  miter-jointed  hopper,  and  gb'c  and  gb'f  those 
for  a  butt-jointed  one.  At  c"f  b'  c,  is  shown  an  outline  of  the 
butt  joint,  and  at  c  c'"a'  b'  that  of  the  miter  joint. 

DIMENSIONS  OF  FURNITURE. 

Chairs  and  Seats.— Height  of  the  seat  above  the  floor,  18  in.*, 
depth  of  the  seat,  19  in. ;  top  of  the  back  above  the  floor, 
38  in.  Chair  arms  are  9  in.  above  the  seat.  A  lounge  is 
6  ft.  long  and  30  in.  wide. 


250 


BOOFim. 


Tables. — Writing  and  dining  tables  are  made  2  ft.  5  in. 
high.  Dining  tables  extend  from  12  to  16  ft.,  by  means  of  a 
sliding  frame.  There  should  be  2  ft.  clear  space  between  the 
frame  and  the  floor. 

Bedsteads. — These  are  classed  as  single,  3  to  4  ft.  wide; 
three-quarter,  4  ft.  to  4  ft.  6  in. ;  and  double,  5  ft.  wide.  All 
bedsteads  are  from  6  ft.  6  in.  to  6  ft.  8  in.  long  inside.  Foot¬ 
boards  are  2  ft.  6  in.  to  3  ft.  6  in.,  and  headboards  from  5  ft.  to 
6  ft.  6  in.  high. 

Other  Furniture. — For  bureaus  convenient  sizes  are;  3  ft.  .c 
in.  wide,  1  ft.  6  in.  deep,  2  ft.  6  in.  high  ;  or  4  ft.  wide,  1  ft.  8 
in.  deep,  3  ft.  high.  Commodes,  or  night  stools,  are  1  ft.  6  in. 
square  on  the  top,  and  1  ft.  6  in.  high.  Chiffoniers  are  3  ft. 
wide,  1  ft.  8  in.  deep,  4  ft.  4  in.  high.  Cheval  glasses  are  made 
about  5  ft.  6  in.  high,  2  ft.  wide.  Washstands  of  large  size  for 
portable  bowl  and  pitcher  are  3  ft.  long,  1  ft.  6  in.  wide,  and 
2  ft.  7  in.  high.  Small  sizes  are  2  ft.  8  in.  long.  Wardrobes  are 
from  6  ft.  9  in.  to  8  ft.  high,  from  1  ft.  5  in.  to  2  ft.  deep,  and 
from  3  ft.  to  4  ft.  6  in.  wide.  Sideboards  are  from  5  to  6  ii. 
long,  about  2  ft.  2  in.  deep  and  3  ft.  3  in.  high.  Upright  pianos 
vary  from  4  ft.  10  in.  to  5  ft.  6  in.  in  length,  from  4  ft.  to  4  ft.  9 
in.  in  height,  and  are  about  2  ft.  4  in.  deep.  Square  pianos  are 
about  6  ft.  8  in.  long  by  3  ft.  4  in.  deep. 


ROOFING. 


SLATING. 

A  good  slate  should  present  a  bright,  silk-like  luster,  and 
should  emit  a  clear  metallic  ring  when  tapped ;  if  it  is  soft, 
it  will  present  a  dull,  lead-like  surface,  and  emit  a  muffled 
sound.  When  cut,  the  edges  should  show  a  fibrous-like 
texture,  free  from  splinters,  and  the  material  should  not 
show  signs  of  being  either  brittle  or  crumbly.  It  is  this 
element  in  slate,  which  may  be  called  its  temper,  that  largely 
defines  its  value;  if  brittle  or  too  hard,  the  slate  will  be 
liable  to  fly  to  pieces  when  being  squared  and  punched,  or 
to  be  readily  broken  when  being  nailed  in  place.  If  the  slate 


ROOFING . 


251 


is  soft,  it  will,  by  absorbing  moisture,  be  liable  to  be  attacked 
by  frost,  so  that  the  edges  will  crumble  away,  and  the  slates 
will  work  loose,  owing  to  the  nail  holes  becoming  enlarged. 

There  are  many  varieties  of  color  in  slate,  due  to  the  pres¬ 
ence  of  iron  and  mineralized  vegetable  substances.  The 
pronounced  colors  are  bluish  black,  blue,  red,  and  green, 
while  many  tints  of  these  shades  exist,  blending  into  grays 
and  purples. 

The  commercial  classification  is  based  on  straightness, 
freedom  from  curled  and  warped  surfaces,  smoothness  of 
surface,  and  uniformity  of  color  and  thickness.  The  best 
way  of  judging  the  classification  is  to  examine  samples  of 
the  various  grades.  First-class  slate  should  be  hard  and 
tough,  non-absorbent,  unfading,  straight-grained,  free  from 
ribbons  and  other  imperfections,  and  of  uniform  color 
throughout.  No  better  test  of  the  weathering  qualities  of 
slate  can  be  contrived  than  the  simple  one  of  examining 
roofs  where  it  has  been  in  service  for  several  years. 

The  sizes  of  slate  range  from  6  in.  X  12  in.  to  16  in.  X  24  in., 
there  being  about  25  different  sizes.  The  size  to  select 
depends  on  the  character  of  the  edifice  and  its  location; 
for  ordinary  dwellings,  a  common  size  is  8  in.  X  16  in.  The 
thickness  of  slate  is  about  T3g  in.,  or  5  to  the  inch  ;  for  extra- 
strong  roofs,  slates  }  in.  thick  are  used,  while  with  the  larger- 
sized  slates,  the  thickness  is  |  in.  or  more.  Slate  weighs 
175  lb.  per  cu.  ft.,  and  if  A"  slates  are  used,  the  weight  of  the 
material  on  the  roof  will  average  6?  lb.  per  sq.  ft.  of  surface 
covered.  Slates  are  sold  by  the  square,  meaning  that  this 
quantity  will  cover  100  sq.ft,  of  roof  surface;  an  ordinary 
railroad  car  has  a  capacity  of  between  40  and  50  squares. 

The  roof  being  devised  for  protection  against  the  elements, 
particularly  rain  and  snow,  the  steeper  the  pitch,  the  more 
effective  will  be  its  power  to  shed  them ;  while  the  wind  will 
not  so  readily  blow  rain  under  the  courses,  nor  strip  them  off 
so  easily.  Where  slates  arc  small  and  light,  and  exposed 
to  violent  winds,  the  greater  the  necessity  for  increasing  the 
pitch.  Experience  shows  that  the  minimum  pitch  for  slate 
roofs  varies  with  the  size  of  the  slate.  The  pitch  may  be 
expressed  either  by  the  angle  which  the  roof  makes  with  the 


252 


ROOFING. 


horizontal,  or  by  the  ratio  of  the  height  of  the  ridge  to  tne 
span ;  the  latter  expression  is  the  one  generally  employed. 
(See  Table  VII,  page  68. )  For  large  sizes  of  slate  the  pitch  should 
not  be  less  than  21°  50',  or  one-fifth ;  for  medium  sizes,  26°  33', 
or  one-fourth ;  and  for  the  smaller  sizes,  33°  41',  or  one-third. 

Slates  are  laid  on  either  strips  or  boarding;  the  latter 
costs  the  most,  but  the  results  justify  the  extra  cost.  Close 
boarding  makes  the  roof  a  better  non-conductor  of  heat,  and 
is  required  for  strength  where  thin  slates  are  used.  In 
Fig.  1  is  shown  a  sectional  view  of  a  roof  on  a  frame  build¬ 
ing,  where  theslates 
are  nailed  to  strips 
a.  These  strips  are 
usually  from  1  to 
1£  in.  thick  and 
2y  or  3  in.  wide, 
and  are  well  nailed 
to  the  rafters ;  the 
distance  between 
centers  of  the  strips 
should  be  equal  to 
the  gauge  or  ex¬ 
posed  portion  of  t  he 
slate.  The  lowest 
strip  is  thicker  than 
the  others,  so  as  to 
tilt  the  first  course 
enough  to  insure  a 
close-fitting  joint 
between  the  first 
two  thicknesses.  In 
commencing  to  slate,  the  first  course  is  laid  double,  the  lower 
course  being  laid  with  the  back  or  upper  surface  of  the  slate 
downwards.  The  length  of  this  course  will  be  equal  to  the 
gauge  plus  the  lap.  The  lap  is  the  distance  that  the  upper 
slate  overlaps  the  head,  or  upper  end  of  the  second  slate 
below  it,  and  should  not  be  less  than  3  in.,  although  slaters 
sometimes  use  only  a  2"  lap.  The  gauge  or  exposed  length 
of  the  slate  is  equal  to  half  its  length  after  deducting  the  lap. 


ROOFING. 


253 


There  are  several  ways  of  nailing  the  slate,  either  near  the 
head  or  at  the  shoulder,  in  which  the  distance  of  the  holes 
from  the  head  will  he  slightly  less  than  the  gauge  of  the  slate, 
to  enable  them  to  clear  the  head  of  the  one  underneath. 

Another  method  of  laying  slate,  where  economy  is  desired, 
is  that  known  as  half  slating ,  in  which  a  space  is  left  between 
the  edges  of  the  slate  in  each  course  equal  to  one-half  the 
width  of  the  slate.  By  this  method,  only  two-thirds  of  the 
usual  number  are  required  to  cover  a  given  surface.  This 
class  of  work  is  adapted  for  covering  sheds,  and  while 
serviceable  under  ordinary  conditions,  will  not  be  water¬ 
tight  under  the  action  of  driving  storms  of  rain  and  snow. 

Slate  nails  have  large  flat  heads,  so  as  to  have  a  good  hold 
on  the  slate ;  their  lengths  vary  with  the  thickness  of  the 
slate,  and  are  usually  called  3-penny  or  4-penny*,  having 
lengths  of  1£  in.  and  If  in.,  respectively ;  the  proper  length 
should  be  twice  the  thickness  of  the  slate  plus  the  thickness 
of  the  boarding.  To  prevent  rust,  slate  nails  are  usually  gal¬ 
vanized  iron  or  steel ;  sometimes  they  are  tar-coated.  For 
extra-good  work,  copper  nails  are  used. 

For  other  data  on  Slating,  see  page  351. 


TIN  ROOFING. 

There  are  two  kinds  of  tin-roof  coverings  in  common  use, 
namely,  flat  seam  and 
standing  seam.  In  the  for¬ 
mer  method  the  sheets  of 
tin  are  locked  into  one  an¬ 
other  at  the  edges,  and 
nailed  to  the  roof-boards  as 
shown  in  Fig.  2.  Six  or 
eight  1"  wire  nails  are  Fig.  2. 

allowed  to  the  ordinary 

sheet.  The  seams  are  flattened  with  wooden  mallets  and 
soldered  water-tight.  The  seams  constitute  the  weakest  part 

*  The  term  penny  as  applied  to  nails  is  a  corruption  of  the 
original  form  in  which  the  nails  were  defined  as  3-pound, 
4-pound,  etc.,  meaning  that  1,000  of  the  nails  weighed 
3  pounds,  4  pounds,  etc.,  respectively. 

Q 


254 


ROOFING. 


of  a  flat  tin  roof,  and  should  therefore  he  made  and  soldered 
with  great  care.  The  tinner  should  not  hurry  the  soldering, 
for  time  is  required  to  properly  “sweat”  the  solder  into  the 
seams,  Resin  is  the  best  flux ;  chloride  of  zinc  or  other  acids 
should  not  be  used.  A  better  method  of  fastening  the  sheets 
to  the  roof  is  by  means  of  tin  cleats  about  1£  in.  X  4  in. 
These  are  nailed  to  the  roof,  and  locked  over  the  upper 
edge  of  the  sheet,  about  15  in.  apart. 

Standing-seam  roofing  is  that  in  which  the  sloping  seams 

are  composed  of  two  upstands  in¬ 
terlocked,  and  held  in  place  by 
cleats.  They  are  not  soldered,  but 
are  simply  locked  together,  as 
shown  in  Fig.  3.  The  sheets  of  tin 
are  first  double-seamed  and  sol¬ 
dered  together  into  long  strips 
that  reach  from  eaves  to  ridge. 
One  edge  is  turned  up  about  1£  in.  and  the  other  about  1£  in. 
The  cleats  are  placed  about  15  or  18  in.  apart.  When  the 
upstands  and  cleats  are  locked  together  the  standing  seam 
is  about  1  in.  high. 

Before  laying  tin,  the  uneven  edges  of  the  boarding  should 
be  smoothed  off  and  the  boarding  covered  with  at  least  one 
thickness  of  sheathing  paper  or  dry  felt,  to  form  a  cushion 
and  otherwise  protect  the  tin.  Knot  holes  in  the  boarding 
should  be  covered  with  pieces  of  heavy  galvanized  iron. 
Only  the  best  quality  of  tin  should  be  used,  and  it  should  be 
painted  on  the  under  side  before  it  is  laid. 

The  outer  edges  of  the  tin  should  be  turned  over  the 
upper  edge  of  the  cornice,  and  clasped  to  a  strip  of  hoop  iron ; 
or,  where  it  connects  with  a  metal  gutter,  the  two  should  be 
locked  and  soldered.  Where  a  tin  roof  abuts  a  chimney  or 
wall,  the  tin  should  be  turned  up  sufficiently  to  prevent 
water  from  rising  over  it.  This  upstand  should  be  counter- 
flashed  with  sheet  lead;  and  abutting  a  wooden  wall  it 
should  be  turned  up  against  the  boarding,  and  the  siding  or 
shingles  laid  over  it.  The  tin  should  also  be  turned  up 
against  all  balcony  posts,  and  the  edges  at  the  angles  weu 
soldered. 


Fig.  3. 


ROOFING. 


255 


The  roof  should  he  painted  within  a  few  days  after  it  Is 
laid,  either  with  red  lead  in  linseed  oil,  or  a  good  asphaltum 
paint,  particular  care  being  taken  to  scrape  off  all  resin  before 
the  paint  is  applied. 

There  is  little  or  no  difference  between  the  methods  of 
laying  tin  or  copper  roofing.  The  most  important  point  to  be 
considered  in  copper  roofing  is  to  have  the  copper  thoroughly 
tinned  before  commencing  to  solder  it. 

For  other  data  on  Tin  Roofs,  see  page  353. 


GRAVEL  ROOFS. 

The  rafters  should  be  spaced  close  enough  to  make  the 
roof  firm,  when  planked  or  boarded.  For  sheathing,  tongued- 
and-grooved  lumber  is  preferable  ;  and  in  any  case  the  plank 
or  roof  boards  should  be  laid  closely— making  close  joints, 
both  at  edges  and  ends— and  should  be  free  from  holes  or 
loose  knots,  and  securely  nailed  to  the  rafters.  Over  the 
sheathing  should  be  laid  four  layers  of  roofing  felt,  the  first 
course,  next  the  eaves,  being  five  layers  thick.  Each  suc¬ 
cessive  layer  should  be  lapped  at  least  f  its  width  over  the 
preceding  one,  and  firmly  secured  with  cleats.  The  quantity 
of  felt  per  100  sq.  ft.  of  roofing  should  be  net  less  than  70  lb. 
The  surface  under  the  outer  layer  of  the  first  course,  and 
under  each  succeeding  layer,  as  far  back  as  the  edge  of  the 
next  lap,  should  be  well  covered  with  a  thin  coating  of 
cement,  in  no  case  applied  hot  enough  to  injure  the  woolly 
fiber  of  the  felt.  Over  the  entire  surface  should  be  spread  a 
good  coating  of  cement,  amounting  in  all  (including  that 
used  between  the  layers)  to  about  10  gal.  per  100  sq.  ft.,  heated 
as  before  specified.  While  the  cement  is  hot,  it  should  be 
completely  covered  with  a  coating  of  dry  slag,  granulated 
and  bolted  for  the  purpose,  no  slag  being  used  that  will  not 
pass  through  a  (pinch  mesh,  and  none  smaller  than  will  be 
caught  by  a  1-i nch  mesh.  All  chimneys  and  walls  that  pro¬ 
ject  above  the  roof  should  be  flashed  and  countcrflashed 
with  zinc  or  copper. 

Gravel  roofs  form  a  very  durable  and  inexpensive  covering, 
but  are  not  suitable  for  any  but  practically  fiat  surfaces. 


256 


ROOFING. 


GUTTERS. 

In  Fig.  4  is  shown  a  strong  and  durable  box  gutter, 
suitable  for  either  a  frame  building  or  for  a  brick  or  stone 

stru  cture,  baying  a 
wooden  cornice.  A  series 
of  lookouts  are  nailed  to 
the  wall  studs  (or  built 
into  the  brickwork  or 
stonework) ,  forming  a 
solid  base  for  the  cornice 
and  gutter.  The  width 
of  the  lookouts  may  be 
varied,  to  obtain  the 
grade  for  the  gutter  bed, 
or  it  may  be  uniform, 
strips  being  nailed  to  the 
upper  edges  of  the  pieces. 
On  a  gable  roof  the  cover- 
plate  over  the  crown 
mold  should  be  kept  in 
line  with  the  sheathing 
on  the  Toof  slope.  In  lining  this  gutter,  if  a  strip  of  hoop 
iron  is  tacked  to  the 
fillet  of  the  crown 
mold,  with  its  lower 
edge  kept  £  in.  below 
the  mold,  the  lining 
maybe  tightly  clasped 
over  the  strip,  and 
face  nailing  dispensed 
with,  thus  making  a 
neat  and  durable  job. 

The  lining  should 
pass  behind  the  eave 
mold,  but  need  not  be 
carried  up  the  slope. 

The  insertion  of  a 
triangular  strip  at  the 
angle  of  the  gutter  bed  and  the  wall  is  of  advantage,  as  the 


ROOFING. 


257 


gutter  is  more  readily  cleaned  by  the  wash  than  with  a  square 
corner.  The  end  of  the  gutter  is  closed  at  the  gable,  so  that 
the  crown  mold  can  run  up  the  facia  and  be  continuous ;  it 
is  usual  to  leave  a  space  of  from  4  to  6  in.  between  the  closed 
end  and  the  gable  facia. 

Figs.  5  and  6  show  methods  of  forming  standing  gut¬ 
ters,  the  former  being  adapted  for  shingled  roofs,  and  the 
latter  for  either 
shingle  or  slate 
roofs.  It  is  impor¬ 
tant  to  insert  the 
tilting  fillet  in  both 
cases,  for  two  rea¬ 
sons:  First,  to  ob¬ 
tain  the  tilt  for  the 
lower  double  course 
so  that  the  bed  of 
the  second  course 
will  lie  close  to  the 
back  of  the  lower 
course ;  and  second, 
to  form  a  drip  at 
the  edge  of  the 
lower  course,  so 
that  water  will  not  Fig.  6. 

be  drawn  up  by 

capillary  attraction  under  the  shingle  or  slate  and  pass  over 
the  upper  edge  of  the  flashing.  These  are  durable  forms  of 
gutters,  but  they  have  the  disadvantage  of  acting  as  guards, 
retain  snow  on  the  roof,  and  mar  to  some  extent  the  appear¬ 
ance  of  the  roof  planes. 

Trough  gutters  of  wood,  tin,  or  copper  are  frequently 
used,  and  where  securely  fastened  in  place,  below  the  drip 
line  of  the  roof  covering,  give  good  results.  Gutters  should 
have  a  pitch  of  in.  per  lineal  foot,  wherever  practicable,  so 
that  the  bed  of  the  gutter  will  be  well  cleansed  during  a  rain 
fall.  Where  the  pitch  is  less  than  stated,  it  is  difficult  to  flush 
the  dust  out  of  the  pockets  formed  by  the  “  kinking’  of  the 
gutter  lining. 


258 


PLASTERING. 


PLASTERING. 


Plastering  consists  in  the  application  of  a  plastic  material 
called  mortar,  to  the  walls  and  ceilings  of  a  building.  The 
plaster  is  either  laid  directly  on  the  face  of  the  wall,  or  it  may 
be  spread  oyer  a  grille  base  of  wood  or  metal  strips  calico 
lath,  the  edges  of  which  are  sufficiently  separated  to  allow 
the  mortar  to  pass  through  and  fold  over  on  the  inner  fane 
thus  forming  a  key,  to  hold  the  substance  in  position. 


LATHING. 

On  brick  or  stone  walls,  lathing  is  usually  attached  to 
vertical  furring  strips,  1  in.  thick  by  2  in.  wide,  set  at  12"  or 
16"  centers.  By  this  means  there  is  a  clear  air  space  between 
the  plaster  slabs  and  the  wall,  thus  insuring  a  continually  dry 
surface,  which  would  otherwise  be  liable  to  dampness.  In 
the  case  of  walls  in  frame  buildings,  the  lath  is  attached 
directly  to  the  studs  forming  the  framing  of  the  walls.  The 
ceiling  lath  may  be  nailed  directly  to  the  under  edges  of  tne 
joists,  or  attached  to  cross-furring,  similar  to  that  used  on  the 
walls,  set  at  right  angles  to  the  joists  and  fixed  at  12"  centers. 
By  the  latter  method  better  results  are  obtained,  as  the  warp¬ 
ing  of  the  joists  does  not  affect  the  lath.  Lath  may  be  either 
split  or  sawed ;  the  former  gives  a  better  wall,  as  there  are  no 
cross-grained  fibers  to  reduce  the  strength,  while  in  the  latter 
such  fibers  make  the  lath  curl  and  warp  from  the  absorp¬ 
tion  of  moisture  from  the  mortar ;  being  cheaper,  however, 
sawed  lath  is  generally  used.  Lath  made  of  pine,  spruce, 
or  hemlock,  should  be  straight-grained,  well  seasoned,  free 
from  sap  and  rot,  clear  of  shakes  and  large  or  loose  knots, 
and,  to  prevent  the  subsequent  discoloration  of  the  plaster, 
it  should  be  free  from  live  knots  and  resinous  pockets. 
The  regular  size  of  a  lath  strip  is  £  in.  X  1J  in.  X  4  ft.,  the 
length  regulating  the  spacing  of  the  furring  strips,  studs,  and 
joists.  Lath  is  nailed  in  place  in  parallel  rows,  the  edges 
being  kept  a  full  |  in.  apart,  to  enable  the  soft  plaster  to  be 
pressed  through  and  form  a  key.  The  ends  should  not  lap, 


PLASTERING. 


259 


but  be  butt-jointed  and  flush  ;  continuous  joints  should  not 
occur  on  one  support,  but  the  lathed  surface  should  be  divided 
into  panels  from  15  in.  to  18  in.  wide,  and  the  joints  be  made  to 
break  on  alternate  supports,  as  shown  by  the  panel  abed  in 
Fig.  1,  page  262,  otherwise  continuous  cracks  will  be  liable  to 
disfigure  the  plaster.  The  lath  is  usually  attached  to  joists 
and  studs  with  cut  or  wire  nails,  about  1|  in.  in  length  and 
having  large  flat  heads,  one  nail  being  used  at  each  support. 
The  nails  should  be  galvanized,  to  prevent  the  moisture  from 
attacking  the  iron  and  causing  them  to  rust,  as  well  as  caus¬ 
ing  large  yellow  blotches  to  appear  on  the  surface  of  the 
plaster. 

There  are  several  metallic  substitutes  for  the  wood  lathing, 
such  as  wire  netting,  crimped,  perforated,  and  expanded 
metal,  all  of  which  possess  much  merit,  and  are  preferable 
to  wood. 

The  carpenter  fixes  plaster  grounds  2  in.  wide,  shown  at 
e,  e,  to  the  masonry  and  framework,  for  the  attachment  of  the 
joiner  work.  Plaster  casings  are  also  placed  around  window 
openings,  and  false  jambs  at  doonvays.  For  3-coat  work,  the 
plaster  grounds  on  brick  or  stone  walls  that  are  to  be  coated 
on  the  solid  wall  should  be  f  in.  thick,  and  those  for  lathed 
surfaces  l  in.  ;  at  no  point  should  the  surface  of  the  solid 
wall  or  that  of  the  lathing  approach  the  face  of  the  grounds 
nearer  than  the  regulation  thickness  for  the  plaster,  which 
will  thus  be  about  1  in. 


PLASTERING. 

Materials.— The  substances  which  enter  into  the  composi¬ 
tion  of  mortar  depend  upon  the  nature  of  the  surface  to  be 
coated,  the  order  in  which  the  layers  are  applied,  and  the 
desired  finish.  For  ordinary  work  they  are  lime  paste,  sand, 
hair,  and  plaster  of  Paris. 

Lime  is  the  product  of  the  calcination  or  burning  of  lime¬ 
stone.  The  material  is  heated  in  a  kiln  until  it  emits  a  red 
glow,  thus  expelling  the  carbonic  acid  and  moisture ;  the 
residue  is  quicklime,  lumps  of  which,  after  being  removed 
from  the  kiln,  are  called  lime  shells.  In  preparing  the 
mortar,  the  lime  shelly  arc  deposited  in  a  woodeu  slaking 


260 


PLASTERING. 


box,  and  are  liberally  sprayed  with  water ;  they  soon  begin 
to  swell,  crackle,  and  fall  into  a  powdery  mass.  This  process 
is  called  slaking  and  the  powrdered  substance  is  slaked  lime  ; 
during  the  process,  the  lime  increases  from  two  to  three 
times  in  bulk  and  much  heat  is  given  out,  which  transforms 
the  excess  of  moisture  into  steam.  Mortar  is  usually  mixed 
by  manual  labor,  but  on  extensive  works  and  in  cities  it  is 
often  prepared  by  mortar  mills,  a  more  thorough  incorpora¬ 
tion  of  the  ingredients  and  a  tougher  paste  being  produced 
by  the  machine  process. 

Sand  may  be  procured  from  the  natural  deposits  in  pits  or 
along  river  shores.  It  should  be  clean ;  this  can  be  deter¬ 
mined  by  rubbing  a  moistened  quantity  of  it  between  the 
hands ;  the  grains  should  be  sharp  and  angular,  not  round  and 
polished.  Where  the  sand  is  coarse,  it  should  be  screened  to 
the  desired  fineness,  by  being  passed  through  a  sieve.  It 
should  be  free  of  salt,  otherwise  it  vTill  attract  and  retain 
moisture ;  this  presence  can  be  detected  by  tasting.  Sand  is 
mixed  in  the  mortar  for  economy,  and  to  check  the  exces¬ 
sive  shrinkage  of  the  lime  paste.  The  sand  in  the  mortar 
increases  its  bulk,  while  sufficient  strength  is  retained,  if  each 
grain  is  well  enveloped  in  a  film  of  the  paste. 

Hair  is  employed  to  bind  the  paste  together  and  to  render 
it  more  tenacious.  Cattle  or  goat  hair  is  used  for  this  purpose, 
but  the  latter  is  considered  the  best.  The  hair  should  be  long, 
free  from  grease  and  dirt,  of  sound  quality,  and  beaten  up  if 
matted.  Owing  to  the  presence  of  salt  in  salted  hides,  hair 
taxen  therefrom  is  undesirable. 

Plaster  of  Paris  is  obtained  from  gypsum,  by  gentle  calcina¬ 
tion.  It  is  very  soluble  in  water,  which  renders  it  unfit  for 
external  use,  but  it  is  valuable  for  cornice  molds  and  enrich¬ 
ments,  and  is  also  used  in  several  plastic  mixtures.  The 
great  value  of  plaster  of  Paris  is  that  paste  made  from  it 
rapidly  sets  and  acquires  full  strength  in  a  few  hours.  Its 
volume  expands  in  setting,  making  it  a  good  material  for  fill¬ 
ing  chinks  and  holes  in  repair  work. 

Mixing  the  Materials. — The  composition  of  the  successive 
coats  are  generally  classified  as  coarse  stuff ,  fine  stuff,  plasterers' 
j>utty,  gauged  stuff ,  and  stucco.  For  all  of  them  it  is  esseq- 


PLASTERING. 


261 


tial  that  the  lime  should  he  thoroughly  slaked.  In  much  of 
the  lime  used  there  are  more  or  less  overburnt,  hard,  obsti¬ 
nate  nodules  which  resist  the  permeation  of  water,  and  fail  to 
disintegrate;  these  must  be  removed  from  the  lime  by  screen¬ 
ing,  otherwise  a  pitted  appearance  of  the  finished  work  will 
invariably  ensue  from  the  future  slaking  of  the  particles. 

Coarse  stuff,  used  for  the  first  coat,  is  composed  of  from  one 
to  two  measures  of  sand  to  one  of  slaked  lime.  The  lime 
paste  and  hair  are  well  mixed;  then,  after  adding  the  sand, 
the  mass  is  worked  together  with  a  hoe,  until  the  materials 
are  completely  combined.  The  mixture  is  then  piled  in  a 
heap  for  a  week  or  ten  days,  to  allow  it  to  sour  or  ferment,  the 
lime  expending  its  heat  and  becoming  effectually  slaked. 
The  lime  and  sand,  if  mixed  while  the  lime  is  still  hot,  pro¬ 
duces  a  much  tougher  mortar,  though  some  authorities  hold 
that  the  sand  should  be  added  last,  after  the  hair,  which,  to 
prevent  being  charred  by  hot  lime,  is  always  mixed  in  the 
mortar  after  the  lime  has  been  cooled.  One  pound  of  hair  is 
usually  added  to  every  2  or  3  cu.  ft.  of  mortar,  according  to 
requirements,  it  being  essential  to  add  more  for  ceiling  stuff 
than  for  walls.  The  consistency  of  the  prepared  mortar 
should  be  such  that  when  the  paste  is  made  to  fold  over  the 
edge  of  the  trowel  it  wTill  hang  well  together. 

Fine  stuff  is  the  pure  lime  which  has  been  slaked  to  a  paste 
by  the  addition  of  a  small  quantity  of  water,  after  which  it  is 
further  diluted  until  it  is  as  thin  as  cream.  When  the  lime 
held  in  suspension  has  subsided,  the  excess  of  water  is 
drained  off,  and  the  moisture  allowed  to  evaporate  until  the 
stuff  is  sufficiently  stiff  for  use.  When  desired,  a  small 
quantity  of  white  hair  is  added. 

Plasterers’  putty,  which  is  always  used  without  hair,  is 
practically  fine  stuff,  but  the  creamy  paste,  having  been 
strained  through  a  fine  sieve,  has  become  much  more  velvety. 

Gauged  stuff  consists  of  about  f  of  the  foregoing  putty  and 
about  j-  of  plaster  of  Paris,  which  causes  the  mixture  to  set 
quickly,  so  that  it  must  be  immediately  used,  not  more  than 
can  be  applied  in  20  or  30  minutes  being  prepared.  An 
excess  of  plaster  in  the  mixture  will  cause  the  coat  to  crack. 
Tin's  is  used  gs  a  finishing  coat  for  walls  and  ceilings,  and 


262 


PLASTERING. 


also  for  running  cornices ;  for  the  latter  work,  equal  pro¬ 
portions  of  putty  and  plaster  are  used. 

Stucco,  for  interior  work,  consists  of  |  fine  stuff  and  j  sand, 
and  is  used  as  a  finishing  coat,  the  mixture  being  whipped 
and  reduced,  by  the  addition  of  water,  to  a  thin  paste. 

Application. — For  3-coat  work,  the  process  of  applying  and 
finishing  the  layers  will  he  described  in  the  order  in  which 
they  are  applied.  The  coarse  stuff  is  taken  in  batches  from 

the  souring  pile, 
tempered  to  the 
proper  degree  of 
firmness,  shov¬ 
eled  into  hods, 
carried  to  the 
rooms,  and  depos¬ 
ited  on  the  mortar 
board,  as  at  /, 
Fig.  1.  A  quan¬ 
tity  of  mortar  is 
placed  on  the 
hawk  g,  by  means 
of  the  trowel  h, 
then  slices  of  the 
mortar  are  spread 
firmly  and  evenly 
over  the  surface 
of  the  lathing. 
The  mortar 
should  he  tough,  hold  well  together,  and  soft  enough  to  be 
pressed  between  the  lath,  bulging  out  behind  and  forming 
the  key.  The  thickness  of  the  layer  should  be  fully  £  in.;  in 
cheap  work  it  is  often  only  a  skim  coat,  and  it  is  hot  unusual 
to  see  the  lath  through  it.  After  the  coat  has  somewhat  hard¬ 
ened,  it  is  scratched  over  diagonally  by  wooden  comb-like 
blades,  as  i,  i ;  from  this  fact  the  first  layer  is  often  called  the 
scratch  coat.  The  grooves  fulfil  the  same  function  as  the  spaces 
between  the  lath,  to  allow  a  good  key  for  the  subsequent  layer. 

The  second  coat,  consisting  of  fine  stuff,  to  which  a  little 
hair  is  sotnqtipaes  added,  is  applied  when  the  scratch  cop,t  hfts 


PLASTERING. 


263 


become  sufficiently  firm  to  resist  pressure ;  the  second  layer 
is  called  the  brown  or  floated  coat,  because  its  surface  is  worked 
by  means  of  boaM-shaped  trowels,  called  floats.  It  is  also 
known  as  the  straightening  coat,  since  all  the  wall  surfaces  are 
straightened  and  made  true.  This  is  effected  by  first  toiming  a 
series  of  plaster  hands,  called  screeds,  5  or  6  in.  wide,  on  the 
surface  to  be  floated.  The  surfaces  adjacent  to  the  angles  are 
carefully  plumbed  up  from  the  plaster  grounds,  but  kept  about 
i  in.  back  from  the  face,  to  allow  for  the  finishing  coat.  Sim¬ 
ilar  screeds  are  formed  along  the  ceiling  angles ;  these  screeds 
are  made  straight,  and  coincide  with  those  at  the  opposite 

angles.  Intermediate  horizontal  and  vertical  screeds  are  then 

formed  between  the  screeds  adjacent  to  the  ceiling  and  the 
plaster  grounds ;  these  are  usually  placed  from  4  to  8  ft.  apart, 
and  are  gauged  to  line  by  means  of  a  straightedge.  The 
screeds  thus  form  a  system  of  framing  which  has  been  reduced 
to  a  true  plane ;  the  panels  are  then  filled  in  flush  with  the 
screeds,  and  firmly  rubbed  down  with  a  two-handled  float, 
called  the  derby.  The  surface  is  then  worked  over  with  a 
wooden  hand  float,  the  coat  being  firmly  compacted  by  inces¬ 
sant  rubbing ;  when  the  coat  becomes  dry  during  the  process, 
it  is  moistened  with  water,- applied  with  a  wide  brush.  A 
close,  firm  layer  can  be  obtained  only  by  the  thorough,  labori¬ 
ous  operation  of  pressing  and  rubbing  the  particles  ot  the 
mortar  together.  The  ceiling  surfaces  are  treated  m  a  similar 
manner,  and  the  screeds  are  carefully  leveled  so  as  to  secure 
true  and  level  planes.  In  order  to  form  a  key  for  the  subse¬ 
quent  coat,  the  surfaces  are  scratched  over  with  a  broom.. 

Where  cornices  are  desired,  they  are  run  before  the  finis  - 
ing  coat  is  put  on  ;  where  the  molded  surfaces  do  not  project 
more  than  2  in.,  the  body  may  be  of  coarse  stuff,  but  where 
the  projection  is  in  excess  of  this,  a  cradling  of  brackets 
and  lath,  made  to  conform  to  the  general  profile,  should  be 
arranged  for  its  support.  Cornice  molds  are  made  of  galva¬ 
nized  iron,  or  zinc,  attached  to  a  wooden  back,  which  m  urn 
is  secured  to  guide  and  brace  strips.  Longitudinal  strips 
are  attached  to  the  wall  either  by  nails  or  a  layer  of  plaster 
of  Paris,  and  on  this  the  mold  guide  runs.  The  coarse  duff 
is  made  to  conform  to  the  approximate  profile  with  a  muffled 


264 


PLASTERING. 


mold,  that  is,  by  forming  a  layer  of  plaster  of  Paris  along  the 
edge  of  the  mold,  about  }  in.  in  thickness  ;  or  an  extended 
profile  can  be  cut  out  of  zinc  and  attached,  temporarily,  to 
the  mold.  When  the  coarse  stuff  has  been  properly  profiled, 
the  surface  is  coated  with  gauged  stuff  and  carefully 
worked  over  with  the  correct  mold,  until  an  exact  and 
perfect  finish  is  obtained.  The  internal  and  external  angles 
cannot  be  finished  by  means  of  the  molds,  but  require  to  be 
carefully  molded  and  mitered  by  hand,  using  steel  plates 
called  jointing  tools. 

There  are  several  kinds  of  finishing  coats,  such  as  troweled 
stucco,  rough  sand  finish,  hard-finish  white  coat,  etc.  In  all 
cases  the  material  is  applied  to  the  wall  in  the  form  of  a  stiff 
paste,  by  means  of  a  steel  trowel,  and  is  spread  uniformly  over 
the  surface  to  a  thickness  of  about  f-  in. 

Troweled  stucco,  consisting  of  fine  stuff  and  sand,  to  which 
a  little  hair  may  be  added,  is  thoroughly  polished  to  a  glazed 
finish  with  a  trowel,  the  surface  being  kept  moist  by  water 
applied  with  a  brush. 

Rough  sand  finish  can  be  produced  on  the  stucco  by  cover¬ 
ing  the  hand  float  with  a  piece  of  carpet  or  felt,  which  will 
cause  the  sand  to  raise  and  present  the  characteristic  sand¬ 
paper  surface. 

Hard-finish  white  coat  consists  of  gauged  stuff,  smoothed  and 
polished  with  the  steel  trowel ;  as  this  material  sets  rapidly, 
care  must  be  taken  to  observe  that  the  second  coat  is  well 
dried,  otherwise  the  unequal  shrinkage  will  cause  hair 
cracks  to  occur  all  over  the  finishing  coat. 

A  similar  finish  may  be  obtained  by  the  use  of  plasterers’ 
putty,  mixed  with  a  small  proportion  of  white  sand,  and 
where  desired  a  little  white  hair  may  be  added ;  this  will  give 
a  more  durable  finish,  but  it  will  not  set  so  quickly,  and  it 
requires  a  more  thorough  working  than  the  former  finish. 

The  space  between  the  plaster  grounds  and  the  floor  is 
usually  finished  with  a  scratch  and  a  brown  coat  of  plaster, 
so  as  to  prevent  air-currents  entering  the  room  from  the 
channels  between  the  furring  strips ;  in  cheap  work  this 
filling  is  omitted,  the  space  being  covered  by  the  skirting  or 
base. 


SANITARY  MAXIMS. 


265 


PLUMBING. 


SANITARY  MAXIMS. 

1.  General  water-closet  accommodation  should  never  he 
placed  in  cellar  or  basement,  but  should  be  located  where 
plenty  of  daylight  and  ventilation  can  be  obtained,  and  should 
open  to  the  outer  atmosphere  either  direct,  or  by  air-shafts  at 
least  3  ft.  square. 

2.  To  prevent  damp  cellars,  subsoil  drains  should  be 
employed  where  necessary.  They  must  be  effecti\  ely  ti  apped 
from  sewers  or  house  drains,  and  some  means  must  be  em¬ 
ployed  to  maintain  a  seal.  A  check-valve,  or  back-water 
trap  should  be  used  to  prevent  a  back  discharge  of  sewage 
into  them,  should  the  drains  become  choked. 

3.  The  arrangement  of  all  drainage  or  vent  pipes  should 

be  as  direct  as  possible. 

4.  If  there  is  a  sewer  in  a  street,  every  building  should 
connect  to  it  separately. 

5.  Where  the  soil  is  natural,  the  house  sewer  may  be  of 
vitrified  earthemvare  pipe,  uniformly  bedded  and  jointed 
with  Portland  cement  and  clean  sharp  sand.  This  pipe  must 
run  straight,  and  must  have  a  clear  bore. 

6.  If  the  soil  is  filled  in  or  made,  the  house  sewer  must  be 
of  extra-heavy  cast  iron,  asphalt-coated ;  of  wrought  iron, 
galvanized,  and  asphalt-coated ;  or  of  brass  pipes,  to  avoid 
leakage  by  a  settlement  of  the  earth. 

7.  When  it  is  necessary  to  run  a  private  sewer  to  connect 
with  a  sewer  in  another  street,  it  should  belaid  outside  the 
curb  of  the  street  which  the  buildings  face,  not  across  lots 
where  buildings  may  in  future  be  erected. 

8.  The  main  house  drains  should  be  run  above  the  ce  ar 
floor  when  possible,  and  be  secured  against  the  cellar  walls 
supported  upon  piers  built  under  each  joint,  or  suspended 
from  the  cellar  ceiling  by  adjustable  hangers. 

9.  If  house  drains  must  be  run  under  the  cellar  floors  they 
should  be  laid  in  straight  runs,  and  clean-outs  or  inspection 


266 


PLUMBING. 


fittings  should  be  placed  at  each  branch  or  change  in 
direction. 

10.  All  changes  in  direction  should  be  made  with  curved 
pipes  or  Y  branches  and  or  £  bends. 

11.  Old  sewers  should  never  be  employed  for  new  build¬ 


ings  unless  first  ex¬ 
amined  and  tested 
by  the  smoke  ma¬ 
chine. 


12.  All  house- 
drainage  system? 
should  be  discon¬ 
nected  from  city 
sewers  by  means  of 
a.  mi  'n  disconnect¬ 
ing  crap,  as  shown 
in  Fig.  1. 


Fig.  1. 


If  the  sewage  from  a  country  building  delivers  into  a 
sea,  a  river,  or  open  space,  the  main  drain  trap  may  often  be 
advantageously  omitted.  A  fresh-air  inlet  must  always 
accompany  a  main  drain  trap. 

13.  Fresh-air  inlet  orifices  must  be  at  least  15  ft.  from  the 
nearest  window  or  door,  and  no  cold-air  box  for  a  furnace 
should  be  so  placed  as  to  draw  air  from  them. 

14.  All  vent  outlets  should  discharge  at  least  2  ft.  above 
the  highest  part  of  a  roof  ridge,  coping,  or  light-shaft,  and  as 
far  as  possible  away  from  the  light-shaft  and  all  water  tanks. 

15.  Vent  pipes  above  roofs  must  be  4  in.  in  diameter  or 
larger,  and  no  cowls  or  vent  caps  should  be  used. 

16.  Vent  pipes  passing  up  through  a  low  roof,  and  within 
30  ft.  of  any  windows  in  taller  adjoining  buildings,  should  be 
extended  to  safe  points  above  the  higher  roofs. 

17.  All  drain,  soil,  waste,  and  vent  pipes  between  the 
main  disconnecting  trap  and  the  vent  outlets  must  be  clear 
and  unobstructed  by  traps,  check-valves,  etc. 

18.  All  house-drainage  work  should  be  as  accessible  as 
possible,  being  placed  either  on  the  faces  of  walls  or  in  air- 
shafts.  When  placed  in  walls  they  should  be  covered  by 
movable  pipe  boards. 


SANITARY  MAXIMS. 


267 


19.  Every  fixture  in  a  building  must  be  separately  trapped 
close  to  each  fixture,  except  where  a  sink  and  washtubs  adjoin 
each  other,  in  which  case  the  waste  pipe  from  the  tubs  may 
join  the  inlet  side  of  the  sink  trap  below  the  water  seal. 

20.  All  fixture  and  other  such  traps  in  a  building  must  be 
back-vented  by  a  separate  pipe  which  may  deliver  into  a 
special  back-vent  stack  at  a  point  about  2  or  3  in.  below  top 
of  fixture,  for  tenement  or  apartment  buildings,  and  at  much 
higher  points,  if  desired,  for  private-residence  work,  but  in 
no  case  at  points  lower  than  bottoms  of  fixtures  or  bowls. 

21.  Where  lead-waste  or  back-vent  branches  connect  to 
cast-iron  stacks,  the  connections  must  be  made  with  heavy 
brass  ferrules  and  wiped  solder  joints ;  if  to  wrought-iron 
or  brass  stacks,  by  means  of  brass-screwed  solder  nipples  pro¬ 
vided  with  a  socket  to  receive  the  lead  pipe  and  form  a  flush 
internal  surface.  All  solder  joints  in  a  plumbing  system 
should  be  “  wiped.” 

22.  Special  precaution  should  be  taken  to  secure  perfect 
joints  between  water-closet  traps  placed  above  the  floor  and 
the  branch  soil  and  vent  pipes  for  same.  Brass  floor  plates 
should  be  used  for  the  floor  connections.  A  smoke  test  is 
necessary  to  prove  these  joints.  Back-vent  horn  or  porcelain 
traps  should  not  be  permitted,  as  they  soon  break  off*.  The 
best  modern  practice  is  to  back-vent  the  soil-pipe  waste  close 
to  the  floor  connection  by  means  of  a  wiped  or  screwed  joint. 

23.  Overflow  pipes  from  all  fixtures  must  connect  to  traps 
on  house  side  of  their  seals. 

24.  All  fixture  safes  should  be  properly  graded  to  a  special 
waste  pipe  which  must  deliver  openly  at  some  point,  such  as 
a  safe-waste  sink  in  the  cellar.  The  outlets  of  these  pipes 
should  be  covered  with  light  flap  valves. 

25.  The  sediment  pipe  from  the  kitchen  boilers  should  not 
be  connected  on  the  outlet  side  of  the  sink  or  other  trap. 

26.  A  separate  small  tank  or  cistern  should  be  employed 
to  flush  every  water  closet,  and  in  no  case  should  any  water 
closet  or  urinal  be  supplied  directly  from  the  street  pressure 
pipes  when  there  is  any  liability  of  a  drawback  in  the  street 
mains. 

27.  One  water  closet,  at  least,  should  be  allowed  for  fifteen 


268 


PLUMBING . 


inmates  of  a  building.  Every  story  of  a  tenement  should 
contain  at  least  one  water  closet. 

28.  Drinking  water  should  be  drawn  directly  from  the 
street  mains.  Tank  water  may  be  used  for  washing  and 
bathing  purposes. 

29.  House  tanks  should  be  made  of  wood,  and  if  placed 
inside  the  building  should  be  lined  with  tinned  and  planished 
sheet  copper. 

30.  Outside  tanks  may  be  circular  and  made  of  cedar 
staves  or  wrought  iron.  Overflow  from  such  tanks  should 
discharge  on  the  roof. 

31.  Overflow  pipes  from  inside  tanks  may  deliver  into  an 
eaves  gutter  if  available,  or  may  be  trapped  and  discharge 
into  an  open  sink.  No  pipe  connecting  to  a  tank  should 
deliver  directly  into  the  drainage  system. 

32.  All  rain-water  leaders,  area  water  boxes,  and  subsoil 
drains,  must  be  trapped  from  the  drainage  system,  and  the 
seals  maintained. 

33.  In  all  cases  where  water  comes  muddy  from  the  mains, 
a  straining  filter  should  be  located  in  the  cellar,  to  filter  all 
water  in  the  building;  muddy  water  clogs  boilers,  water- 
backs,  and  circulation  pipes. 

34.  A  special  germ-proof  filter  is  a  very  valuable  addition, 
and  should  be  placed  at  a  convenient  point,  to  supply  water 
for  drinking  purposes. 

35.  Steam-exhaust,  blow-off,  or  drip  pipes  should  not 
deliver  directly  into  a  drainage  system.  Such  water  should 
deliver  through  a  deep  seal  trap,  and  at  a  temperature  not 
higher  than  100°  F. 

36.  No  privy  vaults  or  cesspools  for  sewage  should  be  per¬ 
mitted  in  any  place  where  water  closets  can  be  connected 
with  a  city  sewer. 

37.  All  privy  vaults  and  cesspools  should  be  frequently 
treated  with  small  quantities  of  disinfectant,  and  should  be 
cleaned  out  thoroughly  and  often. 

38.  All  architects  should  see  that  every  drainage  system, 
when  completed,  is  tested  with  smoke  under  a  pressure  of  at 
least  1  inch  water  column,  because  the  sanitary  arrangements 
are  seldom  perfect  when  this  final  test  is  neglected. 


DRAINAGE  SYSTEM. 


269 


DRAINAGE  SYSTEM. 


PIPES  AND  FITTINGS. 

Cast-Iron  Soil  Pipes. — These  should  be  uniform  in  thickness 
and  homogeneous  throughout.  They  should  be  tested  with 
water  pressure  and  then  coated  with  asphaltum  before  being 
Used. 

These  pipes  come  in  5'  lengths  and  are  known  as  extra 
heavy .  The  maker’s  name  should  preferably  be  cast  on  each 
piece.  Any  pipes  lighter  than  the  following  should  be  rejected. 

Weight  of  Cast-Iron  Soil  Pipe. 


Nominal 

Diameter. 

Inches. 

Weight 
per  Foot. 
Pounds. 

Nominal 

Diameter. 

Inches. 

Weight 
per  Foot. 
Pounds. 

2 

5i 

7 

27 

3 

9* 

8 

33i 

4 

13 

10 

45 

5 

17 

12 

54 

6 

20 

Cast-iron  soil-pipe  fittings  should  correspond  with  the  grade 
of  pipes  used.  They  should  have  easy  curves.  No  sharp  90° 
bends  or  T  branches  should  be  used;  only  obtuse  angle  fit¬ 
tings.  Fittings  are  made  as  staple  goods  at  the  following 
angles :  90°,  45°,  22i°,  11-]°,  and  are  known  as  quarter,  eighth, 
sixteenth,  and  thirty-second  fittings,  respectively. 

Cast-iron  soil-pipe  joints  are  made  with  picked  oakum  and 
molten  lead  calked  solidly  home  in  the  sockets ;  12  oz. 
of  soft  pig  lead  must  be  used  in  each  joint  for  each  inch  in 
diameter  of  the  pipe. 

Wrought-lron  and  Steel  Pipes.— When  used  for  drainage 
purposes  these  should  be  stamped  with  the  maker  s  name. 
They  should  be  galvanized  and  conform  to  the  following 
table : 

R 


270 


PLUMBING. 


Weight  of  Wrought-Iron  or  Steel  Drainage  Pipe. 


Nominal  Diameter. 
Inches. 

Thickness  of  Metal. 
Inches. 

Weight  per  Foot. 
Pounds. 

1* 

.14 

2.7 

2 

.15 

3.6 

2* 

.20 

5.7 

3 

.21 

7.5 

3? 

.22 

9.0 

4 

.23 

10.7 

4? 

.24 

12.3 

5 

.25 

14.5 

6 

.28 

18.8 

7 

.30 

23.3 

8 

.32 

28.2 

9 

.34 

33.7 

10 

.36 

40.1 

11 

.37 

45.0 

12 

.37 

49.0 

Fittings  for  vent  pipes  on  wrought-iron  or  steel  pipes  may 
be  the  ordinary  cast  or  malleable  steam  and  water  fittings. 

Fittings  for  waste  or  soil  pipes  must  be  the  special,  extra¬ 
heavy  cast-iron,  recessed  and  threaded,  drainage  fittings,  with 
smooth  interior  waterway  and  threads  tapped,  so  as  to  give  a 
uniform  grade  to  branches  of  not  less  than  £  in.  per  ft. 

All  joints  must  be  screwed  joints  made  up  with  red  lead, 
and  the  burr  formed  in  cutting  must  be  carefully  reamed  out. 
When  the  male  threads  are  screwed  up  tightly,  the  ends 
should  abut  each  other  in  the  couplings. 

Short  nipples  on  wrought-iron  or  steel  pipe,  where  the 
unthreaded  pipe  is  less  than  in.  long,  should  be  of  the  thick¬ 
ness  and  weight  known  as  extra  heavy  or  extra  strong. 

Brass  Soil,  Waste,  and  Vent  Pipes,  and  Solder  Nipples. — These 
should  be  thoroughly  annealed,  seamless  drawn,  brass  tubing 
of  standard  iron-pipe  gauge.  Connections  on  brass  pipe  and 
between  brass  pipe  and  traps  or  iron  pipe  must  not  be  made 
with  slip  joints  or  couplings.  Threaded  connections  on  brass 
pipe  should  be  tapered  and  of  the  same  size  as  iron-pipe 
threads.  The  following  average  thicknesses  and  weights  per 
lineal  foot  should  be  employed : 


DRAINAGE  SYSTEM. 


271 


Weight  of  Brass  Soil,  Waste,  and  Vent  Pipe. 


Nominal  Diameter. 
Inches. 

Thickness. 

Inches. 

Weight  per  Foot. 
Pounds. 

14 

.14 

2.8 

2 

.15 

3.8 

24 

.20 

6.1 

3 

.21 

7.9 

34 

.22 

9.5 

4 

.23 

11.3 

44 

.24 

13.1 

5 

.25 

15.4 

6 

.28 

20.0 

Brass  ferrules  should  be  bell-shaped,  extra-heavy  cast 
brass,  not  less  than  4  in.  long  and  2i  in.  in  diameter.  The 
least  weight  of  cast-brass  ferrules  and  solder  nipples  should 
be  as  follows : 


Weight  of  Brass  Ferrules  and  Nipples. 


Ferrules. 


Nipples. 


Inside 

Weight, 

Diameter. 

Each. 

In. 

Lb. 

Oz. 

2* 

1 

0 

34 

1 

12 

44 

2 

8 

Inside 

Weight, 

Diameter. 

Each. 

In. 

Lb. 

Oz. 

14 

0 

8 

2 

0 

14 

24 

1 

6 

3 

2 

0 

4 

3 

8 

Particular  care  should  be  taken  to  inspect  all  cast-brass 
ferrules  before  calking  them  in  place,  as  they  are  very  liable 
to  have  sand  holes  in  them,  which  will  cause  annoyance  u 
testing  the  roughing  when  finished. 


272 


PLUMBING. 


Lead  Pipes.— The  weight  of  lead  pipe  should  conform  to  the 
following  table : 

Weight  of  Lead  Soil,  Waste,  and  Vent  Pipe. 


1 


Nominal 

Diameter. 

Inches. 

Weight 
per  Foot. 
Pounds. 

Nominal 

Diameter. 

Inches. 

Weight 
per  Foot. 
Pounds. 

1£* 

2£ 

3 

6 

H 

3 

4 

8 

2 

4 

8 

All  lead  traps  and  bends  should  be  of  the  same  weight 
and  thickness  as  their  corresponding  pipe  branches.  This 
grade  is  known  in  commerce  as  D. 


SIZES  AND  GRADE  OF  SEWERS. 

Sizes  of  Pipes.— House  sewer  and  drain  pipes  must  be  at  least 
4  in.  in  diameter  where  water  closets  discharge  into  them. 
Where  rain  water  discharges  into  them,  the  house  sewer  and 
the  house  drain  up  to  the  leader  connections  should  be  in 
accordance  with  the  following  table  : 


Size  of  Pipe  for  Drainage. 


Diameter. 

Drainage  Area,  Square  Feet. 

Inches. 

Fall  i  In.  per  Ft. 

Fall  i  In.  per  Ft. 

6 

5,000 

7,500 

7 

6,900 

10,300 

8 

9,100 

13,600 

9 

11,600 

17,400 

*  For  flush  pipes  only. 


DRAINAGE  SYSTEM. 


273 


Least  Sizes  of  Soil,  Waste,  and  Vent  Pipe. 


Name  of  Pipe. 


Diameter. 

Inches. 


Main  and  branch  soil  pipes . . 

Main  waste  pipe . 

Branch  waste  pipes  for  kitchen  sinks . 

Soil  pipe  for  water  closets  on  5  or  more  floors 
Waste  pipe  for  kitchen  sinkson  5  or  more  floors 

Bath  or  sink  waste  pipe . . 

Basin  or  urinal  waste  pipe . 

Pantry-sink  waste  pipe  . 

Safe  waste  pipe  . 

Water-closet  trap  . . 

Wash  tubs,  13"  waste  pipe  and  2"  trap  for  set 

of  2  tubs . 

Waste  pipe  for  a  set  of  3  or  4  tubs . 

Main  vents  and  long  branches  . 

Water-closet  vents  on  3  or  more  floors . 

Vent  pipe  for  other  fixtures  on  less  than  7  floors 

Vent  pipe  for  fixtures  on  8  stories  or  less  . 

Vent  pipe  for  9  stories  and  less  than  16  . 

Vent  pipe  for  16  stories  and  less  than  21 . 

Vent  pipe  for  21  stories  and  over  . ; . 

Branch  vents  for  traps  larger  than  2  in . 

Branch  vents  for  traps  2  in.  or  less  . 


4 
2 
2 

5 
3 

13-2 

H-H 

l* 

1  -H 
33-4 

lf-2 

2 

2 

3 

2 

3 

4 

5 

6 
2 
13 


For  fixtures  other  than  water  closets  and  slop  sinks  and 
for  more  than  8  stories,  vent  pipes  may  be  1  in.  smaller  than 
above  stated. 

All  vent  pipes  that  pass  out  through  the  roof  should  be 
increased  one  size  through  and  above  the  roof,  to  allow  for 
ice  accumulations  inside.  In  no  case  should  any  of  these 
pipes  be  less  than  4  in.  in  diameter,  except  in  mild  climates. 
Care  should  be  taken  to  prevent  the  use  of  the  old-fashioned 
cast-iron  vent  caps.  If  the  open  end  must  be  protected,  wire 
baskets  may  be  used. 

The  fresh-air  inlet  should  be  of  the  same  size  as  the  drain, 
up  to  4  in.;  for  and  &'  drains,  it  should  not  be  less  than  4 
in.  in  diameter  ;  for  1"  and  8"  drains,  not  less  than  6  in.  in 
diameter,  and  for  larger  drains  not  less  than  8  in.  in  diameter. 
The  fresh-air  inlet  orifice  should  have  an  area  equal  to  that 
of  the  pipe. 


274 


PLUMBING. 


Fall  for  Drain  and  Waste  Pipes.— The  fall  of  a  drainage  system 
should  be  so  arranged  that  the  velocity  of  the  flow  obtained 
will  be  not  less  than  about  275  ft.  per  ruin.  This  velocity  can 
be  closely  approximated  by  pitching  the  pipes  as  follows : 


Grades  for  Drain  Pipes. 


Diameter. 

Inches. 

Fall. 

Diameter. 

Inches. 

Fall. 

2 

V  fall  in  20'  run 

7 

1'  fall  in  70'  run 

3 

1'  fall  in  30'  run 

8 

1'  fall  in  80'  run 

4 

1'  fall  in  40'  run 

9 

1'  fall  in  90'  run 

5 

1'  fall  in  50'  run 

10 

1'  fall  in  100'  run 

6 

1'  fall  in  60'  run 

DISPOSAL  OF  SEWAGE. 

Sewage  from  buildings  is  disposed  of  chiefly  by  the  follow¬ 
ing  methods:  (1)  By  a  connection  to  the  street  sewer;  (2) 
by  cesspools;  (3)  by  director  indirect  discharge  to  sea,  or 

river,  in  close  proximity  to 
the  buildings.  The  first  plan 
is  always  adopted  in  well- 
regulated  cities,  having  a 
sewer  system,  and  the  work 
is  usually  done  under  the 
supervision  of  city  authori¬ 
ties. 

Cesspools  are  commonly 
used  where  the  first  and 
third  methods  cannot  be  em¬ 
ployed.  They  should  be 
built  water-tight  if  within  200  ft.  of  any  buildings  or  within  100 
yd.  of  any  well.  Fig.  2  shows  common  practice  in  cesspool 
connections.  The  main  drain  from  the  house  is  continued 
through  the  cellar  wall,  a  trap  a  and  fresh-air  inlet  b  being 
placed  outside ;  either  a  vitrified  or  a  cast-iron  sewer  pipe  c 
connects  with  the  cesspool  d ;  and  a  cesspool  vent  e  is  run  up 
the  trunk  of  a  tree.  A  tight-fitting  manhole  cover  should  be 
provided  for  access. 


DRAINAGE  SYSTEM. 


275 


The  size  of  a  cesspool  must  be  determined  by  the  approxi¬ 
mate  amount  of  discharge.  The  least  size  for  a  7-  or  8-room 
house  is  from  6  to  8  ft.  in  diameter,  and  from  10  to  12  ft.  deep. 
The  following  rule  is  in  common  use :  For  a  house  with  G 
rooms  or  less,  make  the  cesspool  6  ft.  in  diameter ;  for  a  7-room 
house,  7  ft.;  increase  the  diameter  6  in.  for  each  additional 
room  up  to  10  rooms ;  then  3  in.  for  each  additional  room  up 
to  20 ;  then  11  in.  for  each  additional  room.  The  general 
depth  is  from  10  to  15  ft.  The  cesspools  should  be  brick-lined, 
domed  over,  and,  if  possible,  provided  with  an  overflow. 


INSPECTION  AND  TESTING  OF  DRAINAGE  SYSTEMS. 

Drainage  systems  in  all  well-regulated  cities  are  inspected 
and  tested  twice  before  being  passed  by  the  authorities  as 
perfectly  sanitary.  These  tests  are :  (1)  A  test  of  the  rough¬ 
ing  in ,  which  consists  of  the  iron  or  brass  drains,  soil,  waste, 
and  vent  lines,  and  sometimes  the  fixture  branches,  also, 
before  any  pipes  are  concealed.  (2)  A  test  of  the  entire 
system  when  the  fixtures  are  all  set,  the  traps  sealed  with 
water,  and  the  work  otherwise  complete. 

The  first  or  roughing  test  is  accomplished  by  closing  all 
branches  and  filling  the  system  with  water  (if  the  weather 
permits),  allowing  the  water  to  stand  in  the  pipes  for  a  cer¬ 
tain  time,  depending  on  the  inspector’s  judgment.  Any  leaks 
can  be  detected  by  water  flowing  from  them.  In  applying 
this  test,  particular  care  must  be  taken  to  use  plugs  in  the 
lower  openings,  which  cannot  be  blown  out  by  the  heavy 
pressures  that  occur  at  these  points. 

Should  the  weather  be  too  cold  for  the  water  test,  the  com¬ 
pressed-air  Aest  is  applied.  In  this  case  air  is  pumped  into 
the  system  until  the  pressure  is  10  lb.  by  the  gauge,  when  a 
valve  between  the  pump  and  the  system  is  closed.  The  pres¬ 
ence  of  leaks  is  made  manifest  by  the  gauge  indicating  a 
decreasing  pressure  as  the  test  continues.  The  location  of 
leaks,  however,  is  difficult  unless  some  pungent  volatile  oil, 
as  ether  or  oil  of  peppermint,  is  allowed  to  vaporize  within 
the  system  and  thus  cause  an  odor  in  the  vicinity  of  the 
leaks ;  or.  the  leaks  may  be  located  by  the  bubbles  formed 


276 


PLUMBING. 


when  a  soap-and-water  solution  is  applied  to  the  joints  with 
a  brush. 

The  final  test  is  the  more  important  one.  The  chief 
objects  are  to  positively  ascertain  (a)  if  the  system  when 
completed  is  gas-tight;  ( b )  if  the  traps  have  perfect  seals; 
(c)  if  every  part  of  the  system  is  trapped  that  should  be 
trapped ;  (cl)  if  any  back-vent  pipes  are  run  into  hollow  par¬ 
titions,  attics,  or  chimneys.  The  test  was  formerly  made  by 
vaporizing  oil  of  peppermint  in  the  drainage  system,  without 
pressure,  trusting  to  a  diffusion  of  a  pungent  vapor  to  indi¬ 
cate  any  leaks.  This  form  of  peppermint  test  is  now  aban¬ 
doned  by  modern  sanitary  engineers  as  untrustworthy,  the 
smoke  test  being  substituted.  This  is  applied  by  blowing 
smoke  through  the  system ;  when  the  smoke  shows  at  the 
various  vent  outlets,  they  are  closed  tightly,  and  the  drains 
are  subjected  to  a  smoke  pressure  of  from  1  in.  to  1£  in.  of 
water  column.  This  pressure  is  sufficient  to  force  smoke 
through  the  most  minute  leaks,  but  is  not  enough  to  blow 
through  the  seal  of  a  good  trap. 

The  best  smoke  machine  for  testing  house  drains  consists 
of  a  double-action  blower,  combined  with  a  smoke-generating 
chamber  furnished  with  a  balanced  floating  cover.  Such  a 
blower  will  force  air  through  the  fire  in  a  steady  stream,  and 
a  uniform  efflux  of  dense  smoke  is  obtained.  The  advantage 
of  the  floating  cover  is  that  it  will  rise  in  its  water  seal  when 
the  desired  pressure  is  obtained,  and  the  pressure  cannot  be 
increased  sufficiently  to  force  the  seals  of  traps,  because  the 
excess  of  smoke  will  escape  to  the  atmosphere  from  under 
the  cover.  The  smoke  machine  may  be  applied  to  the  fresh- 
air  inlet ;  or  to  one  of  the  vent  pipes  above  the  roof— prefer¬ 
ably  to  the  latter,  as  any  smoke  that  escapes  while  lighting  the 
fuel,  which  is  oily  cotton  waste,  cannot  enter  the  building 
and  thereby  spoil  the  test. 

House-drainage  systems  should  be  tested  once  a  year,  and 
a  report  of  the  sanitary  condition  should  be  furnished  after 
each  inspection  and  test.  This  action  is  made  necessary  by 
the  fact  that  the  plumbing  is  often  abused  to  such  an  extent 
as  to  become  dangerous ;  and  settlement  of  buildings  often 
causes  leakage. 


PLUMBING  FIXTURES. 


277 


PLUMBING  FIXTURES. 


BATHS. 

The  most  common  materials  for  baths  are  (a)  porcelain,  or 
earthenware  lined  with  porcelain  enamel ;  ( b )  cast  iron, 
painted  or  lined  with  porcelain  enamel;  (c)  tinned  sheet- 
copper  lining,  inclosed  by  an  iron  or  steel  jacket,  commonly 
called  iron-clad  baths.  Wood-cased  tinned  copper  baths  are 
out  of  date.  Class  (a)  is  used  in  the  very  finest  of  work ; 
class  ( b )  in  plain  substantial  work ;  and  class  (c)  in  cheap 
work.  The  two  kinds  of  baths  which  predominate  are  the 
Roman  shape,  which  slopes  at  both  ends,  and  usually  has 
the  connections  at  the  back,  and  the  French  shape,  which 
slopes  at  one  end  only,  with  connections  at  the  foot.  French 
shapes  are  adapted  to  corners ;  Roman,  for  placing  along 
a  wall,  away  from  corners.  The  following  dimensions  are 
taken  from  a  list  of  baths  made  by  a  reputable  firm : 


Dimensions  of  Baths. 


Dimensions. 

Roman  Shape. 

French  Shape. 

*  Porce¬ 
lain. 

flron 

Enameled. 

t  Porce¬ 
lain. 

flron 

Enameled. 

Ft. 

In. 

Ft. 

In. 

Ft. 

In. 

Ft.  ! 

In. 

Length  . 

5 

0 

4 

6 

4 

6 

1 

4  i 

6 

Length,  including 

fittings . 

4 

10 

4 

10 

Width  outside . 

2 

5 

2 

5 

2 

5 

2 

4 

Width,  including 

fittings . . . 

2 

9 

2 

9 

Height  on  legs . 

Depth . 

2 

1 

1 

7 

1 

1 

■lJ-ll 

7 

2 

1 

1 

7 

2 

1 

0 

8 

Width  of  roll  rim  ... 

0 

6 

2£ 

0 

3 

29 

*  A  5'  6"  bath  is  the  same  height,  depth,  and  width  of  roll 

rim,  but  is  1  in.  wider.  _  .  .  ., 

f  The  sizes  of  these  baths  increase  by  jumps  of  6  in.,  the 
other  dimensions  remaining  about  the  same. 

I  A  5'  bath  has  same  dimensions  excepting  length  ;  a  <>  f> 
fl,pd  a  6'  bath  are  X  in,  \\14er, 


278 


PLUMBING. 


Porcelain  baths  are  variously  classed  by  different  makers, 
but  usually  alphabetically ;  class  a  means  perfect,  without 
flaw,  warp,  or  twist ;  class  b,  slightly  imperfect,  a  little  warped 
or  rough  in  the  enamel,  but  hardly  perceptible ;  class  c, 
defective,  badly  warped,  cracked,  and  blistered. 

Marble  safes  for  baths  are  countersunk  to  a  depth  of  }  in. 
and  are  H  in.  thick ;  they  usually  project  from  3  to  6  in. 
beyond  the  outside  line  of  the  bath  and  its  trimmings,  and 
should  be  nearly  flush  with  the  floor. 

Spray  baths  and  shower  baths,  furnished  with  hot  and  cold 
water,  should  be  provided  with  a  mixing  chamber  and  a 
thermometer,  the  bulb  of  which  must  be  located  in  the  center 
of  the  current.  Spray  and  shower  combinations  are  supplied 
by  makers  to  fit  their  baths,  but  special  ones  are  also  furnished, 
independent  of  baths.  A  countersunk  marble  or  slate  floor 
slab  3  ft.  G  in.  square,  is  usually  set  under  a  combination,  and 
the  bathroom  floor  is  made  water-tight.  Porcelain  receptors, 
3  ft.  6  in.  square,  9  in.  high,  6  in.  deep,  with  2k  in.  roll  rim,  are 
preferable,  however.  About  20  ft.  of  brass  tubing,  closely  per¬ 
forated  with  very  fine  holes,  is  sufficient  for  a  good  spray. 
A  shower  should  not  be  less  than  8  in.  in  diameter.  The 
height  from  the  floor  to  shower  should  be  about  7  ft.  6  in. 
The  combination  should  be  provided  with  a  3"  waste  pipe, 
and  a  4"  or  5"  flush  strainer  in  the  center  of  floor  slab  or 
receptor. 

Seat  and  foot  baths  vary  in  sizes  and  shapes.  The  following 
are  dimensions  of  well-designed  roll-rim  baths : 


Dimensions  of  Seat  and  Foot  Baths. 


Dimensions. 

Seat  Bath. 

Foot  Bath. 

Ft. 

In. 

Ft. 

In. 

Length . 

2 

3 

1 

10 

Length,  including  fittings  . 

2 

8 

Width  . 

2 

2 

1 

7 

Width,  including  fittings . 

1 

11 

Height,  front . 

1 

0 

1 

5 

Height,  back . 

1 

9 

1 

5 

Depth . 

11 

Width  of  roll  rim . 

2k 

Oi 

*-a 

PLUMBING  FIXTURES. 


279 


They  are  connected  with  a  hot  and  cold  supply  and  waste 
connections,  the  same  as  plunge  baths. 

Rain  baths  are  a  kind  of  shower  bath,  especially  adapted 
for  bathing  establishments,  and  have  the  advantage  over 
plunge  baths  for  such 
places,  in  that  they 
occupy  but  little  floor 
area,  and  that  they  are 
thoroughly  hygienic, 
as  the  same  water  never 
comes  in  contact  with 
the  body  twice. 

In  all  spray,  needle, 
shower,  bidet,  and  rain 
baths,  and  shampoos,  a 
mixing  chamber 
should  be  used.  Such 
a  chamber  is  shown  in 
Fig.  3  ;  cold  water,  en¬ 
tering  through  (a),  and 
hot  water,  through  (&), 
are  admitted  to  the 
chamber  (c)  in  small 
jets  and  thoroughly 
mixed  before  passing 
into  the  discharge  pipe 
(d),  the  top  of  which 
discharges  through  the 
showrer,  or  the  shampoo 
attachment  as  desired  A  thermometer  (e)  has  its  bulb  ex¬ 
tending  into  a  circuit  of  mixing  water,  to  indicate  the  temper¬ 
ature  of  the  mixture.  The  difference  between  shower  and 
rain  baths  is  that  a  shower  falls  in  large  drops  at  low  veloc¬ 
ity,  and  the  rain  comes  in  minute  jets  at  high  \elocit>  . 

Sunken  baths  are  simply  large  pools  sunk  below  the  floor 
level ;  they  are  made  of  wood,  brick,  or  terra  cotta,  and  are 
lined  with  sheet  lead  or  copper,  or  faced  inside  with  enameled 
tiie.  The  dimensions  and  capacity  depend  upon  the  size  of 
the  room.  The  depth  varies  from  2  to  4  ft.  Water  is  usually 


d 


280 


PLUMBING. 


provided  at  the  end,  from  a  point  above  the  floor  level,  as 
from  a  nozzle  attached  against  the  wall.  Waste  and  overflow 
connections  are  provided,  similar  to  ordinary  baths. 


WASH  BASINS. 

Wash  basins  are  known  as  round  and  oval,  and  may  be  had 
with  or  without  overflow  attached.  Sizes  of  round  bowls  are 
10, 12, 13, 14, 15, 16, 17, 18,  and  20  in.  in  diameter,  measured  from 
the  outside  of  the  flange.  Oval  patterns  are  14  in.  X 17  in., 
15  in.  X  19  in.,  16  in.  X  21  in.  The  16"  round,  and  the  15"  X  19" 
oval  basins  are  generally  used.  Wash  basins  should  be  set 
near  windows,  in  a  position  convenient  to  put  a  mirror  over 
them,  so  placed  as  to  have  the  light  from  both  sides. 

Marble  basin  slabs  are  1{  in.  thick,  countersunk  on  top,  and 
have  molded  exposed  edges.  Large  slabs  should  be  1£  in. 
thick.  Basin  slabs  are  right  or  left  hand,  according  as  they 
set  in  a  corner  at  the  right  or  left  hand  as  a  person  faces  the 
basin.  Backs  are  usually  8,  10,  or  12  in.  high,  aprons  5  in. 
deep,  and  the  height  from  top  of  slab  to  floor  is  generally 

2  ft.  65  in.  Corner  basins  should  be 
provided  with  back  and  end  plates ; 
ordinary  basins,  with  back  plate 
only ;  recess  basins,  with  back  and 
two  ends.  Safes  under  basins  are 
the  same  size  as  the  slabs. 


WATER  CLOSETS. 

Pan  and  Plunger  Closets.— These 
have  been  condemned  by  health 
boards  and  sanitary  authorities  for 
the  past  20  years  or  more,  and  should 
never  be  xised ;  any  old  ones  dis¬ 
covered  should  be  replaced  by  closets 
of  modern  construction. 

Hoppers.— Hoppers  or  washdown 
closets  are  designated  as  short  or  long 
hoppers,  according  as  their  traps  are 
above  or  below  the  floor.  Long  hoppers  are  only  used  where 


PLUMBING  FIXTURES. 


281 


there  is  danger  of  the  trap  being  frozen,  in  which  case  the 
traps  are  placed  below  frost  level.  A  long  hopper  is  shown  in 
Fig.  4,  while  Fig.  5  illustrates  a  short  hopper.  They  can  be 


had  in  porcelain,  glazed  earthenware,  or  cast  iron  painted 
or  enameled.  Short  hoppers  are  fitted  with  a  flushing  tank 
overhead  ;  long  hoppers  are  usually  fitted  with  a  valve  below 
frost  level. 

Washout  Closets. — They  consist  of  a  basin  and  trap,  both 
above  the  floor.  They  differ  from  hopper  closets  in  that  the 
water  in  the  basin  is  separate 
from  that  in  the  trap,  as 
shown  in  Fig.  6.  They  are 
generally  used  on  good  com¬ 
mon  work,  and  are  thor¬ 
oughly  sanitary ;  but,  being 
somewhat  noisy,  are  not  so 
desirable  as  siphon  closets 
for  dwellings. 

Siphon  Closets.— They  have 
their  contents  removed  by 
siphonage  through  a  long 
crooked  outlet,  the  w^ater  in 
the  basin  being  employed  as  Fig.  7. 

a  trap.  They  are  almost 

noiseless  in  operation.  There  are  many  kinds  of  these  closets 
on  the  market  but  the  most  reliable  are  the  simple  siphon-jet 


282 


PLUMBING. 


arrangements  with  flushing  rim,  as  shown  in  accompanying 
figure.  Those  having  a  low-down  tank  are  the  most  silent  in 
action.  Pneumatic  siphon-jet  closets  are  too  complicated  to 
be  reliable.  Fig.  7  shows  the  closet  in  action ;  the  dotted 
lines  show  the  water  channels  for  the  flush. 

The  dimensions  of  closets  vary  considerably ;  the  follow¬ 


ing,  however,  is  good  practice : 

Width  of  bowl  over  all . ..13  in. 

Height  from  seat  to  floor. . 17  in. 

Depth  from  wall  to  front  of  seat . 23  in. 


The  distances  from  the  center  of  the  outlet  opening  to  the 
walls,  etc. — or  the  “  roughing-in  ”  dimensions,  as  they  are 
called — vary  with  nearly  every  closet. 

Latrines.— Latrines  are  used  chiefly  for  prisons,  factories, 
etc.,  and  are  set  up  in  ranges  of  two  or  more,  partitions  being 
placed  between  each  latrine,  about  24  in.  apart.  The  waste- 
pipe  section  is  usually  5  or  6  in.  in  diameter,  and  the  flush 
pipe  3  or  4  in.  They  are  flushed  by  a  large  tank,  located 
about  6  ft.  above  the  seat,  the  flush  pipe  being  connected  to 
the  bottom  of  the  latrines.  i 

Closet  Ranges.— Closet  ranges,  used  in  schools,  fa  Tories,  etc., 
are  merely  large  troughs  with  one  outlet  and  a  flushing 
arrangement.  They  should  be  simple  and  have  no  mechanical 
parts  to  get  out  of  order.  There  are  many  different  lands,  but 
the  automatic-supply  range  is  probably  the  best.  The  combi¬ 
nations  are  of  3  lengths,  24,  27,  and  30  in.  between  partitions ; 
height  from  floor  to  top  of  seat,  1  ft.  6  in.;  height  from  floor  to 
top  of  iron  partition,  5  ft.  10  in.;  depth  of  partition,  2  ft.  2  in.; 
width  of  range,  from  front  to  back,  1  ft.  7  in.  They  can  be 
had  painted  or  enameled.  If  a  hot  chimney  is  near,  it  is 
advisable  to  use  local  vent-closet  ranges,  and  in  such  case 
allow  about  15  in.  extra  length  for  a  ventilating  extension. 

Closet  Seats.— Closet  seats  should  be  made  of  hard  wood, 
and  the  grain  arranged  so  that  the  seat  will  not  warp,  sliver, 
or  fall  to  pieces.  Quartered  oak,  in  two  or  three  layers 
crossed,  or  in  one  piece  with  dowels  or  cross-strips,  seems 
to  be  the  best  material.  The  seat  should  be  secured  to  the 
porcelain  bowl.  The  hole  should  taper  from  back  to  front, 


PL  UMBING  FIXTURES. 


283 


and  have  the  shape  and  dimensions  shown  in  Fig.  8.  The 
upper  surface  of  the  seat 
should  be  properly  counter¬ 
sunk. 

Seat  Vents. — Many  closets 
are  provided  with  horns 
above  the  water-line  in  the 
bowl,  for  the  purpose  of  ven¬ 
tilating  the  bowl.  These  are 
of  no  use,  however,  unless  a 
strong,  positive  draft  is  con¬ 
stantly  maintained  in  the 
vent  lines.  The  size  of  vent 
pipeis  preferably  3  in .  for  each 
closet,  and  not  less  than  2  in. 

Two  or  three  closets  may  local  vent  into  a  4"  pipe,  the 
size  of  the  pipe  increasing  with  the  number  of  closets  con¬ 
necting  to  it.  All  closets  having  horns  attached  to  them  for 
back- venting  traps  should  be  discarded,  as  these  horns  easily 
break  off.  All  connections  between  metal  pipes  and  porce¬ 
lain  should  be  bolted  flange  joints,  without  horns. 

Floor  Connections.— The  ordinary  brass-bolted  floor  flange 
makes  a  good  connection,  but  if  it  is  not  perfect  there  is  no 
means  of  knowing  the  fact.  One  of  the  best  floor  connec¬ 
tions  for  a  closet  is  shown  in  Fig.  9.  This  is  a  water-  • 

sealed  floor  connection.  The 
pipe  a  is  continued  1|  in. 
above  the  finished  floor,  the 
end  being  rounded  a-nd  free 
from  burrs.  The  floor  is 
countersunk  to  receive  a 
supporting  flange  b  which  is 
attached  to  the  pipe.  A 
brass  flange  c  compresses  the 
rubber  gasket  d  against  the 
porcelain  when  the  bolts  e 
are  drawn  up.  An  annular 
space  is  thus  formed  around  the  neck  of  the  pipe  a,  which 
fills  with  wmter  at  the  first  operation  of  the  closet,  thus  seal- 


Fig.  9. 


284 


PLUMBING. 


ing  the  connection.  If  the  connection  leaks,  this  water  will 
run  out  on  the  floor ;  if  it  does  not,  gas  cannot  escape. 

Closet  Cisterns.— There  are  a  variety  of  kinds  of  closet  cis¬ 
terns  on  the  market,  some  being  simple  and  others  com¬ 
plicated.  In  choosing  a  closet  tank,  (1)  select  for  flushing 
qualities ;  (2)  quietness  in  action ;  and  (3)  simplicity  of  con¬ 
struction. 

Fig.  10  shows  a  plain  valve  cistern  for  wash-down  closets 

and  hoppers ;  its  dimen¬ 
sions  are  about  23  in.  X  12 
in.  X  10  in.  It  is  provided 
with  a  ball-cock  a  and  an 
outlet  valve  b  which  is 
operated  by  a  lever  c 
bolted  to  a  cross-bar  d, 
the  lever  being  worked 
by  a  chain  pull.  The 
tube  g  forms  an  over¬ 
flow  which  discharges 
into  the  flush  pipe  e.  A  deafening  pipe  /deadens  the  noise  of 
the  incoming  water.  The  volume  of  flush  from  this  tank  is 
irregular,  depending  on  the  time  the  valve  b  is  held  up. 

A  better  arrangement  is  shown  in  Fig.  11.  This  is  a  siphon 
cistern  particularly 
adapted  for  wash-outs 
as  well  as  wash-downs 
and  hoppers;  its  di¬ 
mensions  are  about  19 
in.  X  9  in.  X  10  in.  A 
momentary  retention 
of  the  pull  opens  the 
valve  a  and  starts  the 
siphon,  formed  by  the 
shell  b  suspended 
over,  and  attached  to, 
an  inner  standing  tube, 
which  is  secured  to  the  valve  a.  A  refill  to  the  bowl  is 
obtained  by  a  slot  in  the  lower  end  of  the  siphon  tube 
which  causes  the  siphon  to  break  gradually. 


PLUMBING  FIXTURES. 


285 


An  after-wash  cistern,  shown  in  Fig.  12,  is  suitable  for  seat 
action.  The  lever  is  attached  to  the  seat  in  such  a  manner 
that  when  the  seat  is 
depressed  the  valve  a 
is  closed,  and  the  valve 
b  opens,  causing  a 
flow  from  chamber  c 
into  chamber  d. 

When  the  seat  is  re- 
leased  a  opens,  b 
closes,  and  the  closet  is 
flushed. 

A  refill  float-valve 
cistern  especially  suit¬ 
able  for  siphon-jet 
closets,  and  wash-out  closets  requiring  a  refill  to  bowl,  is  shown 
in  Fig.  13.  When  the  float  a  is  raised  it  remains  buoyed 
up  until  sufficient  water  has  passed  through  the  closet,  when 
it  returns  gradually  to  its  seat.  The  pipe  b  serves  as  an  over¬ 
flow  and  at  the  same  time  gives  an  abundant  refill  to  the  bowl. 

These  cisterns  are  re¬ 
markably  quiet  in  action. 
They  are  made  in  two 
sizes.  Cisterns  with 
valves  away  from  the 
edges  are  preferable,  for 
the  wood  is  liable  to 
warp  and  cause  the  lock¬ 
nuts  to  cut  the  copper. 
Water-closet  floor  slabs 
Fig.  13.  are  about  27  in.  square, 

and  countersunk  around 
the  closet.  When  ordered  in  a  closet  combination  the  hole  is 
cut,  and  the  countersinking  done,  by  the  manufacturer.  They 
can  be  had  in  Italian  or  Tennessee  marble,  and  slate.  These 
slabs  are  sent  with  unpolished  edges  and  corners,  unless  other¬ 
wise  ordered.  When  the  slabs  are  to  be  drilled  for  pipes,  a 
diagram  should  accompany  the  order,  giving  exact  distances 
to  centers  of  openings, 
s 


286 


PLUMBING. 


URINALS. 

Urinal  ranges  are  lipped  troughs  with  partitions  set  2  ft. 
apart.  They  are  most  satisfactory  when  flushed  by  an  auto¬ 
matic-siphon  tank  which  discharges  through  a  large  jet  at  the 
upper  end  and  a  spray  tube  at  the  back.  The  tank  should  be 
at  least  4  ft.  above  the  spray  tube.  The  outlet  to  trough 
should  be  arranged  with  a  siphon  which  will  automatically 
discharge  contents  when  the  supply  tank  discharges.  The 
period  of  automatic  flushes  vary  with  the  water  supply ;  good 
flushes  are  obtained  if  the  interval  is  from  5  to  10  min. 

Urinal  ranges  are  made  of  cast  iron,  either  plain,  painted, 
or,  preferably,  enameled.  The  usual  dimensions  of  a  urinal 
range  are  about  as  follows :  Height  of  partition,  5  ft.  8  in. ; 
width  of  partition,  about  1  ft.  6  in.;  width  of  urinal,  from  back 
to  front  of  lip,  11  in.;  depth  of  trough,  6  in.;  regular  height  of 
lip,  2  ft.;  the  height  for  children  is  1  ft.  2  in. 

Individual  urinals  are  made  of  porcelain  and  are  provided 
with  at  least  two  openings,  one  for  the  flush  and  the  other  for 
the  discharge.  The  best  class  have  perforated  flushing  rims, 
and  overflow  openings  inside.  They  are  known  as  flat  or 
corner  urinals.  The  best  forms  are  those  in  which  the  trap 
is  combined  with  the  bowl,  and  arranged  to  be  connected 
without  any  metal  being  exposed.  The  connection  betwreen 
the  porcelain  and  the  metal  is  usually  water-sealed,  which  is 
advantageous.  The  waste  pipe  is  provided  with  a  flange  and 
bolt  for  making  a  perfect  junction  with  the  earthenwrare. 
When  a  flushing  tank  is  used,  the  combination  is  simple, 
efficient,  and  hygienic. 

Individual  urinals  are  set  in  stalls,  the  height  of  which 
stall  should  be  at  least  5  ft.  6  in.;  width  inside,  2  ft.;  length 
of  partition,  2  ft.  4  in.;  depth  of  middle  partition,  1  ft.  8  in. 
Middle  partitions  stand  on  nickel  plated  brass  legs  about  10 
in.  high.  The  size  of  urinal  cisterns  should  be,  for  2  urinals, 
a  2-gal.  cistern ;  3  urinals,  a  3-gal.  cistern,  etc. 


SINKS. 

Sinks  are  generally  classified  as  kitchen,  pantry,  slop,  and 
stable  sinks,  and  are  made  of  different  materials  and  in 
numerous  sizes  and  shapes. 


PLUMBING  FIXTURES. 


287 


Kitchen  sinks  are  generally  rectangular  in  plan,  and  are 
not  provided  with  ping  and  chain,  or  overflow  openings, 
Special  kitchen  sinks  are  furnished  to  order  with  overflow 
attachments  and  plugs. 

Sizes  of  Cast-Iron  Kitchen  Sinks. 


( Depth  inside;  other  dimensions  outside.) 


Length. 

Inches. 

Width. 

Inches. 

Depth. 

Inches. 

Length. 

Inches. 

Width. 

Inches. 

Depth. 

Inches. 

164 

18 

124 

12 

5 

6 

30 

324 

20 

18 

6 

6 

16 

16 

6 

324 

21 

6 

22 

14 

6 

36 

18 

6 

23 

15 

6 

36 

214 

6 

254 

20 

154 

124 

6 

6 

38 

42 

20 

22 

6 

6 

20 

14 

6 

48 

20 

6 

24 

14 

6 

48 

23 

6 

244 

16 

6 

24 

14 

8 

24 

254 

27 

18 

174 

15 

6 

6 

6 

30 

50 

50 

24 

24 

26 

8 

64 

64 

24 

28 

28 

30 

30 

20 

17 

20 

16 

18 

6 

6 

6 

6 

6 

62 

76 

56 

60 

78 

22 

22 

32 

28 

28 

8 

7 

9 

10 

10 

All  sinks  should  he  fitted  up  open,  tnat  is,  no  wooaworn 
of  any  description  in  the  form  of  boxings  should  be  allowed 
near  them,  for  these  boxings  become  moist  and  foul,  and 
make  breeding  places  for  cockroaches  and  other  vermin. 
If  possible,  the  walls  against  which  sinks  are  set  should  be 
glazed  tile  or  other  material  of  a  non-porous  character. 

Sloping  drain  boards  should  be  provided  at  every  sink, 
Ash  or  oak  from  H  to  2  inches  thick  are  well  adapted  f<* 
drain  boards.  Sinks  that  are  not  cast  with  sloping  bottoms 
should  be  set  so  that  the  bottom  will  have  a  fall  towards  t  e, 
strainer.  The  faucets  should  be  located,  if  possible,  at  the 
end  opposite  the  strainer. 


288 


PLUMBING. 


Sizes  op  Copper  Pantry 

Sizes  of  Cast-Iron  Slop  Sinks. 

Sinks. 

Length. 

Inches. 

Width. 

Inches. 

Depth. 

Inches. 

Length. 

Inches. 

Width. 

Inches. 

Depth. 

Inches. 

16 

20 

20 

24 

30 

36 

36 

23 

36 

48 

48 

60 

16 

14 

16 

20 

20 

18 

21 

15 

21 

20 

20 

20 

10 

12 

12 

12 

12 

12 

12 

15 

16 

12 

17 

12 

12 

12 

14 

14 

14 

16 

16 

18 

18 

20 

16 

20 

24 

24 

30 

30 

5-6 

5-6 

5-6 

5-6 

5-6 

5-6 

5-6 

5-6 

Sizes  of  Porcelain  Sinks. 

Sizes  of  Earthenware 

Length. 

Inches. 

Width. 

Inches. 

Depth. 

Inches. 

Pantry  Sinks. 

Length. 

Inches. 

Width. 

Depth. 

Inches. 

36 

23 

7 

Inches. 

42 

48 

28 

30 

24 

24 

18 

20 

7 

7 

9 

9 

20 

23 

25 

14 

16 

17 

41 

51 

51 

Porcelain  sinks  can  be  had  with  a  plain  top  or  roll  rim. 
Copper  pantry  sinks  are  made  in  either  square  or  oval  pat¬ 
terns  ;  the  former  has  a  flat,  and  the  latter,  a  round  bottom. 
Sizes  for  both  patterns  are  given  in  the  table. 

Pantry  and  kitchen  sinks  should  be  set  2  ft.  6  in.  or  2  ft.  7  in. 
from  the  floor  to  the  top  of  the  cap.  Slop  sinks  can  be  bad 
with  or  without  overflow  and  plug.  These  sinks  should  be 
set  at  such  a  height  that  the  rim  will  be  not  more  than  24  in. 
from  the  floor. 

A  sink  should  be  located  near  a  window  for  light,  near  the 
pantry  or  dining  room  for  convenience,  and  away  from  the 
stove  for  comfort. 


PLUMBING  FIXTURES. 


289 


LAUNDRY  TUBS. 

Laundry  tubs,  generally  speaking,  are  made  of  slate, 
cement,  soapstone,  glazed  earthenware,  or  solid  porcelain. 
Wood,  cast  iron  or  sheet  steel  are  not  suitable  materials  for 
wash  tubs.  Tubs  used  in  tenement  and  apartment  houses 
should  be  provided  with  overflows.  The  height  of  wash  tubs 
from  floor  to  top  of  rim  is  from  32  to  36  in.  The  wringer 
should  be  set  on  the  right-hand  tub. 

The  following  tables  give  the  average  sizes  of  slate  and 
cement  tubs : 


Slate  Tubs. 

Cement  Tubs. 

No. 

In. 

In. 

In. 

No. 

In. 

In. 

In. 

Parts. 

Long. 

Wide. 

Deep. 

Parts. 

Long. 

Wide. 

Deep. 

1 

24 

2A 

16 

2 

48 

21  or  24 

16 

2 

48 

21 

16 

2 

53 

24 

16 

2 

54 

24 

16 

2 

60 

24 

16 

3 

78 

24 

16 

3 

72 

21  or  24 

16 

3 

80 

24 

16 

3 

90 

24 

16 

Earthenware  and  porcelain  tubs  come  separately,  and  are 
connected  up  singly  or  in  sets  of  2,  3,  or  4,  as  required.  They 
arc  made  in  two  sizes,  Nos.  1  and  2,  according  to  the  dimen¬ 
sions  shown  in  the  following  table  : 


Dimensions. 

No.  1. 

No.  2. 

Ft. 

In. 

Ft. 

In. 

Length  for  each  tub  . 

2 

0 

2 

7£ 

Length  required  for  2  tubs . v— 

4 

1 

5 

4 

Length  required  for  3  tubs . 

6 

2 

8 

0 

Length  required  for  4  tubs . 

8 

3 

10 

y 

Width  from  front  to  back . 

2 

■1-1? 

2 

If 

Depth  inside  . 

1 

3 

1 

3 

290 


PLUMBING. 


WATER  SUPPLY  AND  DISTRIBUTION. 


METHODS  OF  SUPPLY. 

The  source  of  supply  of  water  to  a  building  will  depend 
upon  prevailing  conditions  and  the  location  of  the  building. 
City  buildings  are  usually  supplied  from  city  mains,  while 
country  buildings  are  supplied  from  wells,  lakes,  and  streams, 
by  means  of  pumps,  hydraulic  rams,  etc. 

Street  Service.— House  pipes  should  connect  to  the  mains 
by  corporation  stops.  A  stop  and  waste  should  always  be 
placed  under  the  sidewalk  at  the  curb,  and  also  a  separate 
stop  and  waste  upon  the  service  pipe  just  inside  the  cellar 
wall. 

If  the  street  pressure  is  great  enough  to  force  water  to  the 
top  floor  of  a  building,  all  fixtures  are  usually  supplied  with 
both  hot  and  cold  water,  by  street  pressure.  If  the  pressure 
is  too  low,  or  the  supply  intermittent,  a  tank  is  placed  in  the 
attic  to  supply  the  building.  If  the  pressure  is  too  high,  it  is 
customary  to  apply  a  pressure  regulator  in  the  cellar. 

The  sizes  of  street  service  pipes  depend  chiefly  upon  the 
street  pressure  and  the  size  of  building  to  be  supplied.  The 
following  is  common  practice : 


Sizes  of  Street  Service  Pipes. 


Class  of  Building. 

Size  of  Pipe. 
Inches. 

Single  dwellings,  two  or  three  stories  high 

Larger  dwellings . 

Tenement  buildings  and  apartment  houses 
Hotels  and  factories . 

i  or  i 

1  or  li 

H  or  2 

2  and  up 

These  pipes  should  be  increased  one  size  if  pressure  is  low. 

Pumps.— The  amount  of  water  raised  by  single-acting  pumps 
is  estimated  by  multiplying  the  number  of  strokes  whioh 
the  piston  travels  in  one  direction  per  minute  by  the  volume 
displaced  or  traversed  by  the  piston  in  a  single  stroke,  the 
supposition  being  that  the  water  flows  into  the  pump  barrel 


WATER  SUPPLY  AND  DISTRIBUTION.  291 


only  when  the  piston  ascends.  It  has  been  found,  however, 
that  the  column  of  water  does  not  cease  flowing  when  the 
piston  descends,  and  that  the  amount  of  water  delivered  is 
greater  than  usually  supposed ;  in  some  cases,  it  is  nearly 
double  the  theoretical  amount. 

A  column  of  water  34  ft.  high  is  balanced  by  the  pressure 
of  the  atmosphere,  but  in  practice  it  requires  a  very  good 
pump  to  draw  to  a  height  of  28  ft. 

Damping  Hot  Water.— The  height  to  which  hot  water  can 
be  raised  by  suction  is  much  less  than  that  of  cold  water,  the 
height  varying  with  the  temperature.  This  is  due  to  the 
increased  pressure  of  the  vapor.  Where  possible,  the  hot 
water  should  flow  into  the  pump  by  gravity.  The  following 
table  gives  the  maximum  vertical  heights  of  suction  pipes  for 
different  temperatures : 


Absolute  Pres¬ 
sure  of  Vapor. 
Lb.  per 

Sq.  In. 

Vacuum. 
Inches  of 
Mercury. 

Temperature. 

Degrees, 

Fahr. 

Maximum 
Height  of 
Suction. 
Feet. 

1 

27.88 

101.4 

31.6 

2 

25.85 

126.2 

29.3 

3 

23.81 

144.7 

27.0 

4 

21.77 

153.3 

24.7 

5 

19.74 

162.5 

22.4 

6 

17.70 

170.3 

20.1 

7 

15.66 

177.0 

17.8 

8 

13.63 

183.0 

15.5 

9 

11.59 

188.4 

13.2 

10 

9.55 

193.2 

10.9 

11 

7.51 

197.6 

8.5 

12 

5.48 

201.9 

6.2 

13 

3.44 

205.8 

3.9 

14 

1.40 

209.6 

1.6 

The  Hydraulic  Ram.— This  machine  is  employed  to  raise 
water  to  a  point  higher  than  the  source  of  supply ;  it  is  chiefly 
used  where  a  large  flow  of  water  with  a  low  fall  is  obtainable, 
and  raises  part  of  the  water  which  operates  it.  The  efficiency 
varies  with  the  ratio  of  the  rise  of  the  discharge  to  the  fall  oj 
che  drive  pipe,  about  as  follows ; 


292 


PLUMBING. 


Ratio  of  lift  to  fall,  4,  6,  8,  10,  12,  14,  16,  18,  20,  22,  24,  26. 

Per  cent,  efficiency,  72,  61,  52,  44,  37,  31,  25,  19,  14,  9,  4,  0. 

To  obtain  the  highest  efficiency  with  any  fall,  the  dash 
valve  should  be  adjusted  to  close  at  the  instant  the  water  in 
the  drive  pipe  has  attained  its  maximum  velocity. 

A  ram  having  a  discharge  pipe  80  or  100  ft.  long  will  deliver 
about  f  the  quantity  supplied  to  a  height  about  five  times  the 
fall ;  or  ^  the  quantity  supplied  to  a  height  of  ten  times  the  fall. 

If  the  pipes  are  lead,  the  drive  pipe  should  be  of  the  A 
grade,  for  diameters  up  to  2  in.,  and  cast  or  wrought  iron  for 

greater  diameters.  The 
discharge  pipe,  if  lead, 
should  be  of  the  B  grade 
for  rises  of  50  ft.  or  less, 
and  of  the  A  grade  for 
rises  between  50  and 
100  ft.  For  falls  greater 
than  10  ft.,  or  rises  of 
more  than  100  ft.,  the 
pipe  must  be  heavier 
than  just  given.  The 
length  of  drive  pipe 
should  be  from  25  to  50  ft. 
If  the  discharge  pipe  is 
very  long  (say  £  mile) 
a  larger  size  than  given  in  the  table  should  be  used.  With  a 
given  supply  of  water  under  a  great  fall,  the  ram  need  not 
be  as  large  as  for  the  same  quantity  of  water  under  a  less  fall. 
When  large  quantities  of  water  are  to  be  raised,  it  is  better  to 
increase  the  number  of  rams,  in  preference  to  having  one  of 
very  large  capacity.  Several  rams  may  be  set  so  as  to  deliver 
into  one  discharge  pipe,  each  having  a  separate  drive  pipe. 

Cisterns. — These  are  used  to  store  rain  water  under¬ 
ground,  for  use  in  country  buildings.  For  an  ordinary  house 
with  8  rooms  or  less,  located  in  a  climate  where  the  rainfall  is 
not  less  than  30  in.  per  annum,  and  where  very  long  droughts 
do  not  occur,  a  brick  cistern  5  ft.  in  diameter  and  7  ft.  deep 
will  be  large  enough  for  a  family  of  10  people.  Larger  build¬ 
ings  should  be  provided  with  two  or  more  cisterns, 


Sizes  of  Pipe  for  Rams. 


Water  Supply 

Size  of  Pipe. 

to  Ram. 
Gal.  per  Min. 

Drive. 

In. 

Discharge. 

In. 

f-  2 

U-  4 

1 

8 

1 

* 

3-7 

li 

i 

6  -14 

2 

i 

12  -25 

2i 

1 

20  -40 

2i 

li 

25  -75 

4 

2 

WA  TER  S  UPPL  Y  AND  DIS  TRIB  UTION.  293 


Cistern  filters  are  essential  in  all  cases.  Fig.  14  shows  an 
excellent  and  simple  form,  which  may  be  built  a  few  feet 
away  from  the  cistern,  and  con¬ 
nected  to  it  by  the  pipe  /.  The 
filter  well  is  built  of  brick,  laid 
in  1-to-l  Portland  cement  mor¬ 
tar.  and  is  divided  into  two 
compartments  by  a  partition 
slab  a  of  slate  or  flagstone.  The 
bottom  is  inclined  so  that  the 
sediment  will  collect  at  d. 

The  chamber  B  has  a  perforated 
bottom  b,  upon  which  is  placed 


Fig.  14. 


a  course  of  gravel,  then  clean  sand,  and  is  topped  with  gravel 
nearly  up  to  the  level  of  the  discharge  pipe  /.  Rain  water 
enters  A  through  the  pipe  c,  and  deposits  any  mud  that  it  may 
contain,  at  d.  Any  overflow  in  A  is  discharged  through  pipe 
e .  The  water  flows  upwards  through  the  sand  in  chamber  B, 
which  clarifies  it.  The  filter  may  be  easily  cleaned  by  stop¬ 
ping  up  /,  pouring  water  into  B,  and  pumping  out  the  mud 
and  dirty  water  from  A.  Renewal  of  the  filtering  material  is 
thus  seldom  necessary. 


DISTRIBUTION. 

Sizes  of  Water  Pipes  in  Building. 


Supply  Branches. 


To  bath  cocks  . 

To  basin  cocks . 

To  water-closet  flush  tank 
To  water-closet  flush  valve 
To  water-closet  flush  pipes 

To  sitz  or  foot  baths . 

To  kitchen  sinks . 

To  pantry  sinks  . 

To  slop  sinks . 

To  urinals  . . 


Low 

High 

Pressure. 

Pressure. 

Inches. 

Inches. 

*-l 

4-  i 

1_ 

4-  4 

_1 

JL 

i  -n 

l-i 

lf-H 

i-  1 

l 

a 

4-  f 

h~  I 

i 

1-  b 

i- 1 

1-  4 

i-  i 

b-  4 

294 


PLUMBING. 


Kitchen  Boilers. — Iron  boilers,  or  hot-water  storage  tanks, 
should  be  galvanized  both  outside  and  inside,  particularly 
inside.  These  boilers  are  commonly  made  of  mild  steel,  and 
are  not  so  durable  as  the  old-time  wrought-iron  boilers. 
Many  of  the  poorer  grades  become  pitted  very  rapidly,  and 
are  not  to  be  recommended  for  first-class  work.  The  longi¬ 
tudinal  seams  are  either  single  or  double  riveted ;  when  double 
riveted,  the  rivets  should  be  staggered. 

Copper  range  boilers  are  in  every  case  to  be  preferred,  if 
properly  coated  inside  with  block  tin.  They  are  classed  as 
light,  heavy  and  extra  heavy,  the  latter  being  tested  to  150  lb. 
water  pressure.  The  best  forms  of  copper  boilers  are  those 
which  are  reinforced  inside  by  stiffeners  or  braces  so  that 
they  will  not  collapse  when  a  partial  vacuum  is  formed 
within  them. 

Ordinary  steel  or  iron  boilers  are  tested  to  150  lb.  water 
pressure,  and  extra  heavy  ones  to  250  lb.  pressure.  The  latter 
should  always  be  used  when  the  street  pressure  is  more  than 
40  lb.  by  the  gauge,  or  when  a  water  hammer  may  at  any  time 
come  upon  the  plumbing  system. 


Standard  Sizes  of  Galvanized  Boilers. 


Capacity. 

Gal. 

Length. 

Ft. 

Diameter 

In. 

Capacity. 

Gal. 

Length. 

Ft. 

Diameter. 

In. 

18 

3 

12 

48 

6 

14 

21 

3* 

12 

52 

5 

16 

24 

4 

12 

53 

4 

18 

24 

3 

14 

63 

6 

16 

27 

4| 

12 

66 

5 

18 

28 

3* 

14 

79 

6 

18 

80 

5 

12 

82 

5 

20 

32 

4 

14 

98 

6 

20 

35 

5 

13 

100 

5 

22 

36 

6 

12 

120 

6 

22 

36 

4* 

14 

120 

5 

24 

40 

5 

14 

144 

6 

24 

42 

4 

16 

168 

7 

24 

47 

4i 

16 

182 

8 

24 

The  size  of  boiler  which  should  be  employed  for  any  par¬ 
ticular  work  depends  chiefly  upon  existing  conditions,  such, 


WA  TER  S  UPPL  Y  AND  DISTRIB  UTION.  295 


for  example,  as  the  water  supply  and  the  nature  of  the 
building.  A  safe  rule  is  to  allow  a  35-  or  40-gal.  boiler  for  a 
building  having  one  bathroom,  and  to  add  30  gal.  addi¬ 
tional  capacity  for  every  extra  bathroom.  The  size  can  only 
be  computed  by  first  ascertaining  the  maximum  quantity  of 
hot  water  which  will  be  drawn  off  in  a  given  time,  and  the 
nature  of  the  heating  agents  which  warm  the  water. 

The  size  of  the  waterback  is  another  item  which  cannot 
be  calculated,  because  it  is  based  on  the  size  of  the  boiler  or 


tice  it  is  found  that  about  100  sq.  in.  of  waterback  heating 
surface  in  actual  contact  with  the  fire  is  sufficient  to  give 
good  results  with  a  40-gal.  boiler  if  water  is  plentiful,  and 
with  a  50-gal.  boiler  if  water  is  scarce. 

Boiler  Connections. — These  are  made  in  different  ways,  but 
the  most  common  and  reliable  method  is  shown  at  (n)  in 
Fig.  15.  The  cold  supply  pipe  e  has  a  branch  /  taken  off  to 


296 


PLUMBING. 


supply  the  boiler.  The  return  pipe  g  furnishes  a  supply 
to  the  waterback  a,  and  the  sediment  cock  h  is  used  to 
empty  the  boiler  when  necessary.  The  hot  water  enters 
the  boiler  through  the  flow  pipe  c,  and  rising  to  the  top,  is 
conveyed  to  the  fixtures  through  d.  The  only  objection  to 
this  arrangement  is  that  it  requires  a  long  time  for  the  water 
in  the  boiler  to  become  hot,  because  the  hot  water  continu¬ 
ally  mixes  with  the  cold.  To  overcome  this  trouble,  c  is 
often  connected  to  d  over  the  boiler,  as  shown  in  (b).  But 
the  latter  method  is  also  objectionable,  in  that  circulation 
between  the  range  and  the  boiler  will  cease  when  the  service 
pipe  is  shut  off,  because  the  hot  water  will  siphon  down  to 
the  vent  hole  in  the  top  of  the  inner  tube.  The  waterback 
will  then  blow  steam  through  c  and  d. 


PLUMBERS’  TABLES. 

Fluxes. 


Flux. 

Used  With. 

Metals  to  be  Joined. 

Resin. 

Copper  bit  or 
blowpipe. 

Lead,  tin.  copper, 
brass,  and  tinned 
metals. 

Tallow,  unsalted. 

Blowpipe  or  wiping 
process. 

Lead,  tin,  or  tinned 
metals. 

Sal  ammoniac. 

Copper  bit  or 
blowpipe. 

Copper,  brass,  and 
iron. 

Muriatic  acid. 

Copper  bit. 

Dirty  zinc. 

Chloride  of  zinc. 

Copper  bit  or 
blowpipe. 

Clean  zinc,  copper, 
brass,  tin,  and 
tinned  metals. 

Resin  and  sweet  oil. 

Copper  bit  or 
blowpipe. 

Lead  and  tin  tubes. 

Borax. 

Blowpipe. 

Iron,  steel,  copper, 
and  brass. 

PLUMBERS ’  TABLES. 


297 


Solders. 


Variety. 

Hard. 

Soft. 

Fusing  Point. 

Zinc. 

Copper. 

Silver. 

d 

•rH 

H 

Lead. 

Bismuth. 

Spelter,  hardest  . . 

1 

2 

700° 

Spelter,  hard  . 

2 

3 

Spelter,  soft  . 

1 

1 

550° 

Spelter,  fine  . 

2 

2 

4 

Silver,  hard  . 

1 

4 

Silver,  medium  . 

1 

3 

Silver,  soft . 

1 

2 

Plumbers’,  coarse  . 

1 

3 

480° 

Plumbers’,  ordinary . 

1 

2 

440° 

Plumbers’,  fine  . 

2 

3 

400° 

Tinners’  . . 

1 

1 

370° 

For  tin  pipe  . 

3 

2 

330° 

For  tin  pipe  . 

4 

4 

1 

Weight  per  Foot  of  Lead  Pipe  and  Tin-Lined  Lead  Pipe. 


Inside 

Diam. 

Brooklyn 

A  A 
Extra 
Strong. 

In. 

Lb. 

Oz. 

Lb. 

Oz. 

* 

1 

12 

1 

8 

1*5 

£ 

3 

0 

2 

0 

3 

8 

2 

12 

* 

4 

12 

3 

8 

1 

6 

0 

4 

12 

H 

6 

12 

5 

12 

1£ 

8 

8 

7 

8 

11 

10 

0 

8 

8 

2 

11 

12 

9 

0 

A 

Strong. 

cq 

Medium. 

C 

Light. 

D 

Extra 

Light. 

Lb. 

Oz. 

Lb. 

Oz. 

Lb. 

Oz. 

Lb. 

Oz. 

1 

4 

1 

0 

0 

12 

0 

10 

1 

0 

0 

13 

1 

12 

1 

4 

1 

0 

0 

12 

2 

8 

2 

0 

1 

8 

1 

0 

3 

0 

9 

4 

1 

12 

1 

4 

4 

0 

3 

4 

2 

8 

2 

0 

4 

12 

3 

12 

3 

0 

2 

8 

6 

8 

5 

0 

4 

4 

3 

8 

7 

0 

6 

0 

5 

0 

4 

0 

8 

0 

7 

0 

6 

0 

4 

12 

298 


PLUMBING. 


Weight  of  Sheet  Zinc,  Copper,  and  Lead. 


Zinc. 

Copper. 

Lead. 

Weight, 

Thick- 

Weight, 

Thick- 

Weight, 

perSq.Ft. 

ness. 

per  Sq.Ft. 

ness. 

perSq.Ft. 

Ounces. 

Inches. 

Ounces. 

Inches. 

Pounds. 

.031 

10 

.013 

10 

3 

.046 

12 

.016 

12 

YE 

4 

.053 

14 

.019 

14 

YZ 

5 

.061 

16 

.022 

16 

6 

.069 

18 

.025 

18 

n 

.076 

20 

.029 

20 

15 

8 

Weight  per  Foot  of  Lead  Tubing  and  Waste  Pipe. 


Tubing. 

Waste  Pipe. 

Diameter 

Weight 

Diameter 

Weight 

Diameter 

Weight 

Inches. 

Ounces. 

Inches. 

Pounds. 

Inches. 

Pounds. 

* 

H 

2 

4 

5,  6,  8 

u 

2 

3,  4 

41 

8,  10 

6 

32 

21 

21 

4,  6 

5 

8,  10,  12 

l 

4 

5,  6,  8, 13 

3 

41,  5 

6 

12,  up. 

Weight  of  Brass  Tubing. 


Nominal 

Diameter. 

Inches. 

Weight  per 
Lineal  Foot. 
Pounds. 

Nominal 

Diameter. 

Inches. 

Weight  per 
Lineal  Foot. 
Pounds. 

2, 

.25 

2 

4.00 

I 

4 

.43 

21 

5.75 

t 

.62 

3 

8.30 

1_ 

.90 

31 

10.90 

i 

1.25 

4 

12.70 

l 

1.70 

41 

13.90 

U 

2.50 

5 

15.75 

H 

3.00 

6 

20.60 

N 


PLUMBERS'  TABLES. 


299 


Weight  of  Sheet  Iron. 


o 


U 

<D  . 

n  a> 

£  « 
fro 


1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 

15 


Thickness. 

Inches. 

Black  Iron. 
Weight  per 

Sq.  Ft. 

Pounds. 

Number  of 

Gauge. 

- 

Thickness. 

Inches. 

Black  Iron. 

Weight  per 

Sq.  Ft. 

Pounds. 

Galvanized 

Iron.  Weight 

per  Sq.  Ft. 

Pounds. 

.300 

.284 

.259 

.238 

.220 

.203 

.180 

.165 

.148 

.134 

.120 

.109 

.095 

.083 

.072 

12.0 

11.4 

10.4 

9.5 

8.8 

8.1 

7.2 

6.6 

5.9 

5.4 

4.8 

4.4 

3.8 

3.3 

2.9 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

.065 

.058 

.049 

.042 

.035 

.032 

.028 

.025 

.022 

.020 

.018 

.016 

.014 

.013 

.012 

2.6 

2.3 

2.0 

1.7 

1.4 

1.3 

1.1 

1.0 

0.9 

0.8 

0.7 

0.6 

0.6 

*  0.5 

0.5 

3.0 

2.7 

2.3 

2.1 

1.7 

1.5 

1.3 

1.2 

1.1 

1.0 

1.0 

0.9 

0.7 

0.7 

0.6 

Spacing  of  Lead  Pipe  Tacks. 


Size  of 
Pipe. 
Inches. 


a. 

8 

i 

9 


l 

H 

it 


Vertical  Pipe. 

Hot. 

Cold. 

Inches. 

Inches. 

18 

24 

19 

25 

20 

26 

21 

27 

22 

28 

23 

29 

24 

30 

Horizontal  Pipe. 


Hot. 

Inches. 


12 

14 

15 

16 

17 

18 
18 


Cold. 

Inches. 


16 

17 

18 

19 

20 
21 
22 


Tacks  are  spaced  ciosei  — 
is  much  more  liable  to  sag  when  heated. 


300 


HEATING  AND  VENTILATION. 


Length  of  Wipe  Joints  for  Lead  Pipe. 


Diameter 
of  Pipe. 
Inches. 

Length 
of  Joint. 
Inches. 

Diameter 
of  Pipe. 
Inches. 

Length 
of  Joint. 
Inches. 

Diameter 
of  Pipe. 
Inches. 

Length 
of  Joint. 
Inches. 

* 

2i 

It  water 

3 

2  waste 

2* 

2t 

li  waste 

2 

2j  waste 

2£ 

i 

2i 

li  water 

3i 

3  waste 

2i 

1 

2i 

1|  waste 

2i 

4  waste 

3 

HEATING  AND  VENTILATION. 


STEAM  HEATING. 

A  steam-lieating  system,  with  steam  haying  a  pressure  less 
than  10  lb.  by  the  gauge,  is  called  a  low-pressure  system.  If  the 
steam  is  at  a  higher  pressure,  the  system  is  called  high-pres¬ 
sure  system.  Wh'en  the  water  of  condensation  flows  back  to 
the  boiler  by  gravity  alone,  the  apparatus  is  known  as  a 
gravity-circulating  system.  When  the  boiler  is  run  at  a  high, 
and  the  heating  system  at  a  low,  pressure,  the  condensed 
steam  must  be  returned  to  the  boiler  by  a  pump,  steam  return 
trap,  or  injector. 

The  low-pressure  gravity  circulating  systems  considered 
to  be  the  best  are :  the  two-pipe  system  with  wet  returns ;  the 
two-pipe  system  with  dry  returns  ;  the  one-pipe  system ,  in  which 
all  mains,  branches,  and  risers  are  relieved  into  a  return  main 
below  the  water-line;  and  the  one-pipe  circuit  system,  in  which  all 
pipes  are  run  above  the  water-line.  The  choice  of  any  system 
will  depend  upon  special  conditions  and  requirements. 


RADIATION. 

To  find  the  amount  of  direct  radiating  surface  required  to 
heat  a  room,  basing  calculations  upon  its  cubic  contents, 
allow  1  sq.  ft.  direct  radiating  surface  to  the  number  of  cubic 
feet  shown  in  the  following  table : 


STEA  M  HE  A  TING.  301 

Proportion  of  Radiating  Surface  to  Volume  of  Room. 


Description. 

Cu.  Ft. 

Bathrooms  or  living  rooms,  with  2  or  3  exposures 
and  large  amount  of  glass  surface . 

40 

Living  rooms,  1  or  2  exposures  with  large  amount 
of  glass  surface  . 

50 

Sleeping  rooms  . 

55-  70 

Halls  . 

50-  70 

Schoolrooms  . 

60-  80 

Large  churches  and  auditoriums . 

65-100 

Lofts,  workshops,  and  factories . 

75-150 

The  above  ratios  will  give  reasonably  good  results  on  ordi¬ 
nary  work,  if  the  engineer  uses  proper  judgment  in  allowing 
for  exposures,  leakages  through  building,  etc. 

Proportion  of  Radiating  Surface  to  Glass  Surface:  ^Baldwin’s 

Rule. — Divide  the  difference  in  temperature  between  that  at  which 
the  room  is  to  be  kept  and  the  coldest  outside  atmosphere,  by  the 
difference  between  the  temperature  of  the  steam  pipes  and  i hat  at 
which  the  room  is  to  be  kept.  The  quotient  will  be  the  square  feet 
or  fraction  thereof  of  plate  or  pipe  surface  to  each  square  foot  of 
glass,  or  its  equivalent  in  wall  surface. 

Let  S  =  amount  of  radiating  surface  required  to  counter¬ 
act  the  cooling  effect  of  the  glass  and  its  equiva¬ 
lent  in  exposed  wall  surface  in  square  feet ; 
t  =  difference  in  degrees  F.  between  the  desired  tem¬ 
perature  of  the  room  and  that  of  the  external  air ; 
t\  =  difference  in  degrees  F.  between  the  temperature 
of  heating  surface  and  that  of  the  air  in  the  room; 
s  =  number  of  square  feet  of  glass  and  its  equivalent 
in  exposed  wall  surface. 

Then,  applying  rule,  S  =  -7-  s. 

h 

The  heating  surface  found  by  this  rule  only  compensates 
for  the  heat  lost  by  transmission  through  windows,  walls,  and 


*  This  rule  also  applies  to  hot-water  heating. 


302 


HEATING  AND  VENTILATION. 


other  cooling  surfaces ;  it  does  not  provide  for  cold  air  enter¬ 
ing  the  room  through  loosely  fitting  doors,  windows,  etc., 
for  which  an  ample  allowance  must  be  made.  Some  build¬ 
ings  are  so  poorly  constructed  that  50  per  cent,  or  more  must 
be  added  to  the  amount  of  heating  surface  obtained  by  the 
rule  in  order  to  counteract  the  cooling  effect  of  these  air  leak¬ 
ages.  A  common  practice  is  to  add  25  per  cent,  for  buildings 
of  ordinary  good  construction.  Ample  allowance  should  be 
made  for  rooms  exposed  to  cold  winds.  It  is  usual  to  esti¬ 
mate  about  10  sq.  ft.  of  wall  surface  as  equivalent  in  cooling 
power  to  1  sq.  ft.  of  glass. 


PIPING. 

Sizes  of  Steam  Pipes. 


Radiating 
Surface. 
Sq.  Ft. 

1-Pipe 

Work. 

In. 

2-Pipe 

Work. 

Radiating 
Surface. 
Sq.  Ft. 

1-Pipe 

Work. 

In. 

2-Pi 

Wor 

e 

Steam 

In. 

Ret. 

In. 

Steam 

In. 

Ret. 

In. 

40-  50 

1 

i 

3 

1,600-  2,000 

4£ 

4 

3£ 

100-  125 

li 

1 

i 

2,000-  2,500 

5 

4i 

4 

125-  250 

1£ 

li 

l 

2,500-  3,600 

6 

5 

4£ 

250-  400 

2 

H 

li 

3,600-  5,000 

7 

6 

5 

400-  600 

2£ 

2 

n 

5,000-  6,500 

8 

7 

6 

600-  900 

3 

21 

2 

6,500-  8,000 

9 

8 

6 

900-1,200 

3! 

3 

2| 

8,000-10,000 

10 

9 

6 

1,200-1,600 

4 

3| 

3 

- 

If  the  mains  are  high  above  the  boiler,  and  have  short, 
straight  runs,  small  pipes  may  be  used.  If  they  are  unusually 
low  or  extremely  long  or  crooked,  they  should  be  large.  The 
above  table  will  give  good  r'esults  in  ordinary  systems. 

To  determine  approximately  the  size  of  steam  mains  or 
principal  risers,  allow  1  sq.  in.  of  sectional  area  of  pipe  for  each 
100  sq.  ft.  of  radiating  surface. 

To  determine  the  amount  of  radiating  surface  a  pipe  will 
supply,  allow  100  sq.  ft.  for  each  square  inch  of  sectional  area 
of  pipe. 


STEAM  HEATING. 


303 


Sizes  of  Tappings  for  Prime  Surface  Radiators. 


Direct  Radiators. 

Indirect  Radiators. 

1-Pipe  Work. 

2-Pipe  Work. 

Surface. 

Size. 

Surface. 

Steam. 

Return. 

Surf. 

Steam. 

Ret. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In. 

In. 

Sq.  Ft. 

In. 

In. 

25 

1 

30 

2 

30 

1 

* 

25-  50 

H 

30-  50 

1 

i 

30-  50 

It 

1 

50-  90 

li 

50-100 

It 

l 

50-100 

1* 

H 

100-160 

2 

100-160 

U 

»  1 

100-160 

2 

1* 

DIRECT  RADIATORS. 

Heat  units  emitted  j>er  hour,  per  square  foot  of  external 
surface,  per  degree  of  difference  in  temperature. 

Vertical  Tubes,  Prime  Surface  Radiators. 


Difference 

in 

Temper¬ 

ature. 

F°. 

Tubes  Massed. 

Single  Row  Tubes. 

Height, 

40  Inches. 
B.  T.  U. 

Height, 

24  Inches. 
B.  T.  U. 

Height, 

40  Inches. 
B.  T.  U. 

Height, 

24  Inches. 
B.  T.  U. 

50 

1.29 

1.54 

1.46 

2.01 

60 

1.33 

1.58 

1.50 

2.06 

70 

1.36 

1.62 

1.54 

2.12 

80 

1.39 

1.66 

1.58 

2.17 

90 

1.41 

1.70 

1.62 

2.22 

100 

1.46 

1.74 

1.65 

2.27 

110 

1.49 

1.78 

1.69 

2.32 

120 

1.52 

1.82 

1.73 

2.38 

130 

1.56 

1.86 

1.77 

2.43 

140 

1.59 

1.90 

1.81 

2.48 

150 

1.63 

1.94 

1.85 

2.53 

160 

1.66 

1.98 

1.88 

2.59 

170 

1.69 

2.02 

1.92 

2.64 

180 

1.73 

2.06 

1.96 

2.70 

190 

1.76 

2.10 

2.00 

2.75 

200 

1.80 

2.14 

2.03 

2.80 

210 

1.83 

2.18 

2.07 

2.85 

220 

1.86 

2.22 

2.11 

2.90 

230 

1.90 

2.27 

2.15 

2.96 

240 

1.93 

2.31 

2.19 

3.01 

304 


HEATING  AND  VENTILATION. 


Flue  Radiators— Natural  Draft. 


Radiating  Surface. 

B.  T.  U.  Emitted. 

Total  B.  T.  U. 
Emitted. 

Extended. 
Sq.  Ft. 

Plain. 
Sq.  Ft. 

Extended. 
Sq.  Ft. 

Plain. 
Sq.  Ft. 

Extended. 

Plain. 

57.80 

40.40 

1.65 

1.97 

95.37 

79.58 

6.40 

4.24 

2.05 

2.39 

13.12 

10.13 

63.10 

41.20 

1.39 

1.85 

87.81 

76.22 

7.18 

4.50 

1.90 

2.24 

13.64 

10.08 

INDIRECT  RADIATORS. 

Heat  units  emitted  per  square  foot  of  actual  surface  per 
hour,  per  degree  of  difference  in  temperature. 

Natural  Draft,  Extended  Surfaces. 


Height 
of  Flue. 
Feet. 

Velocity 
of  Air  per 
Second. 
Feet. 

*  B.  T.  U. 
Emitted. 

Height 
of  Flue. 
Feet. 

Velocity 
of  Air  per 
Second. 
Feet. 

B.  T.  U. 
Emitted. 

5 

2.90 

1.70 

30 

6.70 

2.60 

10 

4.10 

2.00 

35 

7.14 

2.67 

15 

5.00 

2.22 

40 

7.50 

2.72 

20 

5.70 

2.38 

45 

7.90 

2.76 

25 

6.30 

2.52 

50 

8.20 

2.80 

Forced  Draft,  Plain  Surfaces. 


Velocity 
of  Air  per 
Second. 
Feet. 

*  B.  T.  U. 
Emitted. 

Velocity 
of  Air  per 
Second. 

Feet. 

\ 

B.  T.  U. 
Emitted. 

Velocity 
of  Air  per 
Second. 
Feet. 

B.  T.  U. 
Emitted. 

3 

3.42 

8 

5.71 

18 

8.50 

4 

4.00 

10 

6.33 

20 

9.00 

5 

4.50 

12 

6.93 

22 

9.42 

6 

4.94 

14 

7.50 

24 

9.79 

7 

5.33 

16 

8.06 

*  A  British  thermal  unit  is  the  quantity  of  heat  necessary 
to  raise  the  temperature  of  1  lb.  of  water  1°  F. 


STEAM  HEATING. 


305 


SIZE  OF  CHIMNEYS. 

Chimneys  are  proportioned  either  to  the  amount  of 
radiating  surface  in  a  building,  or  to  the  horsepower 
required  for  machinery,  or  to  both  combined.  The  draft 
pressure  increases  with  the  height  of  the  chimney.  Boilers 
operating  under  forced  draft  from  fans  or  blowers  do  not 
require  high  chimneys,  except  for  the  purpose  of  conveying 
the  gases  of  combustion  above  the  breathing  zone.  But  in 
all  ordinary  buildings  the  chimneys  should  be  built  suffi¬ 
ciently  high  and  large  so  that  forced  draft  is  not  necessary. 

Size  of  Chimney  for  Given  Amount  of  Radiation,  or 

Horsepower. 


Steam 
Radiation 
Sq.  Ft. 

Horse¬ 

power. 

Diameter,  or  Side,  of  Chimney  in  Inches. 

20  ft. 
High. 

40  ft. 
High. 

60  ft. 
High. 

80  ft. 
High. 

100  ft. 
High. 

250 

2.5 

7.5 

6.8 

6.3 

6.0 

6.0 

500 

5.0 

9.5 

8.8 

8.0 

6.5 

7.4 

750 

7.5 

11.4 

10.3 

9.4 

8.8 

8.5 

1,000 

10.0 

12.8 

11.5 

10.5 

10.0 

9.5 

1,500 

15.0 

15.3 

13.5 

12.5 

11.5 

11.3 

2,000 

20.0 

17.3 

15.3 

14.0 

13.3 

12.5 

3,000 

30.0 

20.5 

18.3 

16.5 

15.8 

15.0 

4,000 

40.0 

23.5 

20.8 

19.0 

17.8 

17.0 

5,000 

50.0 

26.0 

23.0 

21.0 

19.5 

18.5 

6,000 

60.0 

28.5 

25.0 

22.8 

21.3 

20.3 

7,000 

70.0 

30.5 

27.0 

24.5  ' 

23.0 

21.5 

8;  000 

80.0 

32.5 

28.5 

26.0 

24.3 

23.5 

SIZE  OF  BOILERS. 

No  hard-and-fast  rules  can  be  employed  for  determining 
the  heating  capacity  of  boilers  or  for  ascertaining  the  sizes 
best  adapted  for  different  jobs.  The  following  table  is  deduced 
from  practical  tests  and  observations  by  Prof.  Carpenter,  of 
Cornell  University,  and  is  considered  to  be  within  the  limits 
of  safety.  Two  cases  are  taken:  (A)  when  the  rate  of  coal 
consumption  is  10  lb.,  and  ( B )  when  it  is  8  lb.  per  sq.  ft.  of 
grate  surface  per  hour.  The  latter  is  preferable  for  hot-water 
heating. 


Proportioning  Parts  of  Heating  Boilers.— Steam  Heaters. 


306 


HEATING  AND  VENTILATION. 


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10 

100 

80 

300 

240 

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34.5  26.5* 

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33.3 

41.5 

two  4-inch 

34 

7,500 

75 

7  1  9* 

9.5 

95 

76 

285 

ooq 

40.5  31.5* 

32.7  25.6* 

1071  833* 

26.5 

32.5 

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*  Water-tube  boiler. 


EXHAUST-STEAM  HEATING. 


307 


EXHAUST-STEAM  HEATING. 

Exhaust  steam  turned  into  a  heating  system  creates  a  back 
pressure  on  the  engine,  which  must  be  avoided  as  much  as 
possible  by  using  large  steam-distributing  pipes.  A  direct 
connection  to  the  boilers  through  a  pressure-reducing  valve 
must  be  employed,  to  automatically  furnish  steam  when  the 
exhaust  fails ;  and  a  relief  valve  should  be  placed  upon  the 
system  so  that  surplus  exhaust  steam  may  escape.  Before 
the  steam  enters  the  system,  the  20  or  25  per  cent,  of  wrater 
and  oil  it  usually  contains  should  be  removed. 

To  proportion  an  exhaust-heating  system,  it  is  necessary 
to  know  the  weight  of  steam  discharged  from  the  engine,  in 
order  to  determine  how  many  square  feet  of  radiating  surface 
are  required  to  properly  condense  the  steam. 


Weight  of  Water  Used  per  Hour  per  Indicated 

Horsepower. 


Class  of  Non-Condensing  Engine. 

Weight  of  Water. 
Pounds. 

Compound  automatic . 

25 

Simple  Corliss . 

BO 

Simple  automatic . 

35 

Simple  throttling . 

40 

From  these  figures  about  10  per  cent,  must  be  deducted 
for  cylinder  condensation,  etc.,  in  order  to  obtain  the  real 
available  weight  of  steam  for  heating  purposes. 


Ratio  Between  Cubic  Contents  and  Radiator  Surface 
for  Exhaust  Heating. 


Class  of  Building. 

Direct 

Radiation. 

Indirect 

Radiation. 

Blower 

System. 

Dwellings  . 

Offices  . 

Stores  and  shops . . 

Churches,  etc . 

S.  Ft.  C.  Ft. 
1  to  50 

1  to  70 

1  to  100 

1  to  200 

S.  Ft.  C.  Ft. 
1  to  40 

1  to  60 

1  to  80 

1  to  150 

S.  Ft.  C.  Ft. 
1  to  300 

1  to  365 

1  to  500 

1  to  900 

308 


HEATING  AND  VENTILATION. 


The  figures  on  page  307  are  reasonable  averages,  and  allow¬ 
ances  must  be  made  for  exposure,  etc. 

Each  square  foot  of  direct  radiating  surface  gives  off  to 
the  air  around  it  about  H  Thermal  Units  per  hour  per  degree 
of  difference  between  the  temperature  of  the  steam  and  that 
of  the  surrounding  air.  This  is  equivalent  to  about  £  lb.  of 
steam  per  hour ;  or,  from  4  to  4£  sq.  ft.  of  surface  to  each 
pound  of  steam  to  be  condensed. 


HOT- WATER  HEATING. 

The  circulation  in  a  hot-water  heating  system  is  a  move¬ 
ment  of  hot  water  from  the  boiler  to  the  radiators,  where  it 
parts  with  some  heat,  and  a  consequent  movement  of  colder 
water  from  the  radiators  to  the  boiler  to  become  reheated. 
Without  circulation  heat  cannot  be  conveyed  from  the  boiler 
to  the  radiators.  The  velocity  of  circulation  depends  chiefly 
upon :  (a)  the  difference  between  the  mean  density  of  the 
ascending  current  and  that  of  the  returning  current ;  (b)  the 
vertical  height  of  circuit  above  the  boiler  ;  and  (c)  the  resist¬ 
ance  to  flow  due  to  friction,  change  in  direction,  etc.  The 
theoretical  velocity  could  easily  be  computed,  but,  as  it  is 
only  imaginary,  is  of  little  value  to  the  practical  man ;  and, 
further,  the  actual  velocity  bears  no  definite  ratio  to  the 
theoretical. 


RADIATING  SURFACE. 

The  sizes  of  pipes  should  be  governed  by  the  amount  of 
radiating  surface  to  be  supplied,  the  height  of  the  radiators 
above  the  boiler,  and  the  number  of  changes  in  the  direction 
of  the  several  currents.  It  is  considered  safe  practice  to  allow 
from  50  to  100  square  feet  of  direct  radiation  for  each  square  inch 
of  cross-section  in  the  pipe.  If  the  pipes  are  short,  straight,  and 
high,  1  to  100  would  be  allowed  ;  if  long,  crooked,  or  low,  1  to 
50  or  more,  according  to  the  conditions. 

To  determine  the  amount  of  radiating  surface  necessary  to 
easily  warm  a  building  in  all  kinds  of  weather,  and  to  pro¬ 
portion  it  so  that  each  room  will  have  the  required  tempera¬ 
ture  ;it  the  sgjne  time,  are  very  important  points,  requiring 


HOT- WATER  HEATING. 


309 


careful  consideration.  No  rules  can  be  given  applicable  to 
all  cases,  but  for  ordinary  buildings  having  the  average  wall 
and  glass  exposures,  the  following  table  is  found  in  practice 
to  give  good  results,  when  used  with  judgment. 

Ratio  of  Hot-Water  Radiating  Surface  to  Volume  of 

Room. 

Direct  Radiation.  Average  Temperature  in  Radiators,  160°  F. 


Name  of  Room. 


Ratio, 

1  Sq.  Ft.  to 
Cu.  Ft. 


Living  rooms,  one  side  exposed  . 
Living  rooms,  two  sides  exposed 
Living  rooms,  three  sides  exposed. 

Sleeping  rooms  . 

Hall  and  bathrooms . 

Schoolrooms  and  offices . 

Factories  and  stores . 

Auditoriums  and  churches . 


30 

28 

25 

30-  40 
20-  30 
30-  50 
50-  70 
80-100 


For  direct-indirect  radiation  allow  at  least  25  per  cent, 
extra.  For  indirect  radiation  allow  50  per  cent,  extra. 

Due  allowance  must  be  made  for  leakages  through  loose 
doors,  windows,  etc.  _ 


PIPING. 

Sizes  of  Tappings  for  Hot- Water  Radiators. 


Direct  Radiators. 

Indirect  Radiators. 

First  Floor. 

Second  Floor. 

Surface. 

Size. 

Surface. 

Size. 

Surface. 

Size. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In. 

0-15 

f 

0-20 

f 

0-40 

1 

15-50 

1 

20-70 

1 

40-90 

H 

50-100 

H 

70-125 

H 

90-150 

100- 

H 

125- 

H 

150- 

2 

310 


HEATING  AND  VENTILATION. 


Radiating  Surface  Supplied  ba'  Hot-Water  Mains. 

Direct  Radiation.  Fall  of  Temperature,  20°.  Height  of  Circuit , 

from  10  to  15 feet. 


O 

03  CQ 

3  c % 

Total  Estimated  Length  of  Circuit  in  Lineal  Feet. 

<X>'drC 

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• 

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20 

1* 

56 

40 

25 

2 

116 

85 

70 

50 

21 

220 

150 

120 

100 

90 

3 

345 

240 

200 

170 

150 

140 

125  110 

100 

90 

31 

500 

340 

280 

245 

225 

205 

190 

175 

162 

150 

4 

700 

485 

390 

340 

310 

280 

260 

240 

230 

220 

41 

925 

640 

535 

460 

410 

375 

345 

325 

300 

295 

5 

1,200 

830 

700 

600 

540 

490 

450 

420 

400 

380 

6 

1,900 

1,325 

1,100 

950 

850 

775 

700 

650 

620 

600 

7 

2,000 

1,600 

1,400 

1,250 

1,140 

1,050 

975 

925 

875 

8 

1,970 

1,720 

1,550 

1,440 

1,350 

1,300 

1,250 

9 

1,900 

1,800 

1,700 

1,620 

Diameter  of  Radiator  Connections. 
Direct  Radiation.  Fall  of  Temperature,  20°. 


Size  of  pipe  in  inches . 

* 

1 

H 

1* 

2 

2* 

Area  in  square  feet  . 

16 

24 

40 

60 

120 

240 

The  sectional  area  of  the  mains  should  approximate  the 
sum  of  the  area  of  its  branches,  hut  in  many  cases,  particu¬ 
larly  where  there  is  no  indirect  work,  the  sizes  may  be  a 
little  less. 

The  fittings  used  on  hot-water  mains  should  all  have  easy 
curves  and  the  branches  should  be  Y’s,  to  reduce  resistance  to 
a  minimum.  Special  distributing  fittings  should  be  used  to 
induce  circulation  through  radiators  op  the  first  floor. 


HOT- WATER  HEATING. 


811 


Sizes  of  Mains  and  Branches. 

Sizes  of  Main.  Sizes  of  Branches. 

1"  will  supply  two 

11"  will  supply  two  1";  or  one  V  and  two  f". 

Is"  will  supply  two  11";  or  one  11"  and  two  1". 

2"  will  supply  two  11";  or  one  11"  and  two  11". 

21"  will  supply  two  11"  and  one  11";  or  one  2"  and  one  11". 
3"  will  supply  one  21"  and  one  2";  or  two  2"  and  one  1{". 
31"  will  supply  two  21"  ;  or  one  3"  and  one  2":  or  three  2". 
4"  will  supply  one  31"  and  one  21";  or  two  3";  or  four  2". 
41"  will  supply  one  31"  and  one  3";  or  one  4"  and  one  21". 

5"  will  supply  one  4"  and  one  3";  or  one  41"  and  one  21". 

6"  will  supply  two  4"  and  one  3";  or  four  3";  or  ten  2". 

7"  will  supply  one  6"  and  one  4";  or  three  4"  and  one  2". 

•  8"  will  supply  two  6"  and  one  5";  or  five  4"  and  two  2". 

All  flow  and  return  pipes  should  be  of  the  same  size. 

All  pipes  must  rise  from  the  boiler  to  the  radiators  with  a 
pitch  of  at  least  1  in.  in  10  ft. 

The  expansion-tank  capacity  should  be  at  least  ^  that  of 
the  entire  apparatus,  if  it  is  an  open  tank.  Closed  tanks  are 
not  to  be  recommended. 


Radiating  Surface  Supplied  by  Hot-Water  Risers. 
Direct  Radiation.  Fall  of  Temperature ,  20°. 


Diameter 

of 

Story  Where  Heater  is  Located. 

Riser. 

1 

2 

3 

4 

5 

6 

Inches. 

Sq.  Ft. 

Sq.  Ft. 

Sq.  Ft. 

Sq.  Ft. 

Sq.  Ft. 

Sq.  Ft. 

1 

12 

17 

21 

24 

1 

22 

32 

40 

48 

li 

38 

56 

70 

80 

88 

11 

66 

92 

112 

132 

145 

2 

140 

196 

238 

2S0 

310 

21 

240 

328 

400 

470 

515 

3 

350 

490 

595 

700 

770 

850 

31 

510 

705 

860 

1,010 

1,110 

1,215 

4 

700 

980 

1,190 

1,280 

1,540 

1,660 

312 


HEATING  AND  VENTILATION. 


There  is  a  practical  limit  to  the  advantageous  vertical 
length  of  risers,  especially  with  the  smaller  pipes.  If  a 
small  riser  extends  to  a  great  height,  the  friction  become: 
excessive,  and  the  quantity  of  water  delivered  will  he  mucl .  . 
smaller  than  it  would  otherwise  be. 

Limiting  Height  of  Risers. 

Diameter  in  inches .  £  1  H  H  2 

Height  in  feet  . . .  20  30  45  60  80 

The  horizontal  pipes  on  the  upper  floors  of  a  building,  and 
also  the  risers  leading  thereto,  may  be  made  smaller  in 
diameter  than  those  upon  the  lower  floors,  because  the  force 
which  impels  the  water  increases  with  the  height  of  the 
circuits.  The  proper  size  of  a  pipe  having  been  determined 
for  a  given  service  on  the  first  floor,  the  diameter  for  equal 
service  on  higher  floors — the  temperatures  remaining  the- 
same — may  be  found  by  multiplying  by  the  following  factors : 


Story . 2d  3d  4th  5th 

Factor  . 87  .80  .76  .73 


The  area  of  heating  surface  that  may  be  properly  supplied 
by  a  pipe  of  given  diameter  will  increase  as  the  circuit  is 
made  higher.  If  the  area  which  is  known  to  be  right  for 
a  given  size  of  pipe  on  the  first  floor,  be  taken  as  1,  the  areas 
on  the  uppei  floors  will  increase  in  the  following  order : 

Story .  2d  3d  4th  5th 

Proper  area  heating  surface .  1.40  1.70  1.98  2.20 


FURNACE  HEATING, 

It  is  assumed  in  the  following  rules  and  tables  that  the 
average  temperature  of  the  hot  air  in  the  flues  is  about  120°, 
and  that  the  air  is  moved  solely  by  natural  draft. 

A  simple  method  for  proportioning  hot-air  pipes  to  deliver 
a  given  volume  of  air  to  the  several  floors  is  to  assume  that 
1  sq.  in.  of  stack,  or  flue,  area  will  supply  100  cu.  ft.  of  air 
per  hour  at  the  first  tLor,  125  at  the  second  floor,  and  150  at 
the  third  floor. 


FURNACE  HEATING. 


313 


Ratio  of  Area  of  Hot-Air  Pipes  to  Volume  of  Room. 


Rooms. 

Ratio.  1  Sq. 
In.  to  Cu.  Ft. 

First-floor  rooms,  moderate  exposure . 

30 

First-floor  rooms,  great  exposure  . 

20-25 

Second-floor  rooms  . 

25-35 

Third-floor  rooms . 

30-40 

A  more  accurate  method  is  as  follows : 

Rule. — For  rooms  on  the  first  floor,  add  together  the  total  glass 
surface  and  £  the  area  of  the  exposed  walls  in  square  feet,  and 
multiply  the  total  by  1.5;  the  product  is  the  proper  area  of  the  pipe 
in  square  inches.  For  second-story  rooms,  multiply  by  1  to  1.25, 
according  to  the  exposure;  and  for  the  third  story,  by  .75  to  1. 

If  leaders  are  of  considerable  length,  their  area  should  be 
about  x  greater  than  the  connecting  stacks. 

Size  of  Hot-Air  Pipes  and  Registers. 


First-Floor  Rooms. 


o 


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10  X  12 
or 

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8X12 


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14X14 

to 

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to 

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Second-Floor  Rooms. 


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02  ^ 
O-ri  Pi 
n  bx)i— i 
•H  CD 


10X14 

9X12 

8X12 

8X10 


U  Pi 
©M 

ai 

cSjr1 
■r*  P-l 
<+-1 
o 


10- 

9- 

8- 

7- 


CO 

°  a  . 
8  g£ 

mp4 


16X16 

to 

18X20 

14  X  14 
to 

16X16 

10X10 

to 

13  X  14 
7X12 
to 

12X12 


2g>. 

fetes  w 
*53  © 


10 

9 

8 

8 


314 


HEATING  AND  VENTILATION. 


Area  of  Rectangular  Registers. 


Size  of 
Opening. 
In. 


6X10 
8X10 
8X  12 

8X  15 
9X12 
9X  14 
10  X  12 
10  X  14 
10  X  16 
12  X  15 
12  X  19 


Net  Area. 
Sq.  In. 


40 

53 

64 

80 

72 

84 

80 

93 

107 

120 

152 


Size  of 
Opening. 
In. 


14  X  22 

15  X  25 

16  X  24 
20  X  20 
20X24 

20  X  26 

21  X  29 
27  X  27 
27  X  38 
30X30 


Net  Area 
Sq.  In. 


205 

250 

256 

267 

320 

347 

400 

486 

684 

600 


Area  of  Round  Registers. 


Diam  of 
Opening. 

In. 

Net  Area. 

Sq.  In. 

Diam.  of 
Opening. 

In. 

Net  Area. 
Sq.  In. 

7 

26 

16 

134 

S 

33 

18 

169 

9 

42 

20 

209 

10 

52 

24 

301 

12 

75 

30 

471 

14 

103 

36 

679 

VENTILATION. 

Ventilation  is  a  process  of  moving  foul  air  from  any  space 
and  replacing  it  with  fresh  air.  A  positive  displacement, 
however,  does  not  take  place ;  the  incoming  fresh  air  chiefly 
dilutes  the  foul  air  to  a  point  suitable  for  healthful  respira¬ 
tion. 

Pure  air,  such  as  exists  in  the  open  country,  contains 
about  4  parts  of  carbonic  acid  ( C02 )  per  10,000  parts  of  air, 
while  badly  ventilated  rooms  often  contain  as  much  as  80. 


VENTILA  TION. 


315 


parts  of  CO2  per  10,000  of  air.  Hygienists,  after  careful  study, 
have  decided  that  an  increase  of  2  parts  of  C02  per  10,000  of 
air  should  be  accepted  as  the  standard  of  respirable  purity,  and 
any  excess  of  C02  above  this  may  be  considered  as  vitiation. 

Production  of  C02  per  Hour. 


Source. 

Cu.  Ft. 

Adult  man  . . . 

.6 

One  cubic  foot  of  gas,  burning . 

.8 

Ordinary  lamp  . 

1.0 

Candle  . . 

.3 

Taking  the  figures  above  given — 1  parts  of  C02  per  10,000 
parts  of  fresh  air,  and  6  parts  (=  4  +  2)  per  10,000  of  vitiated 
air — as  the  standard  for  proper  health  conditions,  it  is  found 
that  3,000  cu.  ft.  of  fresh  air  per  hour  are  necessary  for  each 
adult  person.  If  a  different  standard  than  6  is  used,  the 
number  of  cubic  feet  per  person  will  be  found  by  dividing 
B,000  by  the  difference  between  this  standard  and  4. 

If  any  lights  deliver  their  products  of  combustion  into  the 
room,  the  amount  of  CO-2  given  off  by  them  should  be  con¬ 
verted  into  its  equivalent  in  men,  thus :  One  ordinary  gas 
light  equals  in  vitiating  effect  about  5f  men,  an  ordinary 
lamp  If  men,  and  an  ordinary  candle  about  f  man. 

It  is  considered  good  practice  to  allow  2,000  cu.  ft.  of  fresh 
air  per  hour  for  each  inmate  of  a  room  or  auditorium.  Hospi¬ 
tals  and  such  places,  where  the  vitiation  is  due  to  exhalations 
from  diseased  or  sick  people,  should  be  provided  with  at  least 
twice  this  amount. 


NATURAL  VENTILATION. 

In  natural  ventilation  systems,  the  drafts  in  the  flues  or 
ducts  are  caused  by  the  difference  in  density  between  the  air 
in  the  ducts  and  the  outer  atmosphere.  The  higher  the  tem¬ 
perature  in  the  ducts,  the  more  rapid  will  the  draft  become. 

In  the  following  table  50  per  cent,  (a  fair  average  in  good 
work)  has  been  deducted  from  the  theoretical  flow,  to  offset 


316 


HEATING  AND  VENTILATION. 


all  ordinary  resistances  in  the  flues,  such  as  friction,  change 
in  direction,  etc.  The  difference  in  temperature  given  in 
the  table  is  that  existing  between  the  outer  atmosphere  and 
the  average  of  the  air  in  the  flue.  Knowing  the  velocity 
per  minute,  and  the  cubic  feet  of  air  per  minute  to  be 
removed,  the  area  of  the  flue  in  square  feet  is  found  by  divi¬ 
ding  the  volume  by  the  velocity. 

Flow  of  Air  in  Flues  per  Square  Foot  of  Section. 

By  Natural  Draft ,  in  Cubic  Feet  per  Minute. 


Height  of  Flue  in  Feet. 


<X> 


a  . 

£  ft 

a) 

10 

Cu.  Ft. 

15 

Cu.  Ft. 

20 

Cu.  Ft. 

30 

Cu.  Ft. 

40 

Cu.  Ft. 

50 

Cu.  Ft. 

60 

Cu.  Ft. 

80 

Cu.  Ft. 

100 

Cu.  Ft. 

10 

108 

133 

153 

188 

217 

242 

264 

306 

342 

15 

133 

162 

188 

230 

265 

297 

325 

375 

420 

20 

153 

188 

217 

265 

306 

342 

373 

435 

485 

25 

171 

210 

242 

297 

342 

383 

420 

485 

530 

30 

188 

230 

265 

325 

375 

419 

461 

530 

594 

40 

216 

265 

305 

374 

431 

482 

529 

608 

680 

50 

242 

297 

342 

419 

484 

541 

594 

680 

768 

60 

266 

327 

376 

460 

532 

595 

650 

747 

842 

70 

288 

354 

407 

498 

576 

644 

703 

809 

910 

80 

308 

379 

435 

533 

616 

688 

751 

866 

972 

90 

326 

401 

460 

565 

652 

728 

795 

918 

1,029 

100 

342 

419 

484 

593 

684 

765 

835 

965 

1,080 

125 

384 

470 

541 

664 

766 

857 

939 

1,085 

1,216 

150 

419 

514 

593 

726 

838 

937 

1,028 

1,185 

1,325 

FORCED  VENTILATION. 

There  are  two  classes  of  forced  ventilation  :  (1)  The  plenum 
system,  in  which  the  air  pressure  in  the  building  is  slightly 
greater  than  that  of  the  outer  atmosphere ;  in  other  words, 
that  system  by  which  air  is  blown  through  the  building  by 
a  fan  or  other  blower  placed  at  the  inlet.  (2)  The  vacuum 
system,  or  that  method  of  removing  foul  air,  and  causing  a 
consequent  inrush  of  fresh  air,  by  an  exhaust  fan  placed  at 
the  outlet  to  the  vent  flue  or  stack.  In  the  latter  system,  the 


VENTILATION. 


317 


air  pressure  in  the  building  is  slightly  lower  than  that  of  the 
outer  atmosphere.  The  plenum  system  is  the  more  whole¬ 
some  and  preferable  method. 

The  capacity  of  a  fan,  that  is,  the  amount  of  air  which  it 
will  deliver,  depends  considerably  upon  the  construction  of 
the  fan,  and  upon  the  resistance  to  the  flow  of  the  air. 

The  following  table  shows  a  safe  capacity  for  some  leading 
forms  of  blowers  and  exhaust  fans,  operating  against  a  pres¬ 
sure  of  1  oz.  per  sq.  in.,  or  If  in.  water,  nearly : 


Diameter  of 
Wheel. 

Ft. 

Revolutions 

per 

Minute. 

Horsepower 

Required. 

Capacity  per 
Minute. 

Cu.  Ft. 

4 

350 

6.0 

10,600 

5 

325 

9.4 

17,000 

6 

275 

13.5 

29,600 

7 

230 

18.4 

42,700 

8 

200 

24.0 

46,000 

9 

175 

29.0 

56,800 

10 

160 

35.5 

70,300 

If  the  resistance  is  greater  than  above  given,  the  required 
capacity  may  he  obtained  by  increasing  the  number  of  revo¬ 
lutions-,  increasing  the  horsepower  correspondingly.  Or,  if  the 
resistance  is  less,  the  required  capacity  may  be  obtained  by 
reducing  the  number  of  revolutions,  with  a  corresponding 
decrease  of  power. 

In  selecting  a  fan,  it  is  advisable  to  choose  a  large  one, 
so  that  it  may  run  easily,  quietly,  and  economically.  A 
small  fan,  which  must  be  run  at  high  speed,  wastes  too  much 
energy,  and  often  makes  a  disagreeable  noise. 

Fresh-air  inlets,  if  near  the  floor,  should  be  so- arranged 
that  the  velocity  of  inlet  will  not  exceed  2  ft.  per  second  ;  a 
higher  velocity  is  considered  a  perceptible  draft.  Higher 
velocities,  however,  are  permissible  if  the  inlets  are  located 
more  than  8  ft.  above  the  flpor.  Vent-flue  inlets  can  safely 
be  made  to  operate  with  a  velocity  of  6  or  8  ft.  per  second, 
without  the  air-current  being  disagreeably  perceptible, 
u 


318 


GAS  AND  GAS-FITTING. 


GAS  AN  D  GAS-FITTI NG. 


GAS. 


KINDS  OF  GAS. 

Coal  gas  is  made  by  heating  bituminous  coal  in  air-tight 
boxes  or  retorts.  The  heat  breaks  up  the  combinations  of 
hydrogen  and  carbon  in  the  coal,  transforming  them  into 
other  compounds,  most  of  which  are  gaseous  at  ordinary 
temperatures.  Among  the  new  compounds  thus  made  are  tar, 
ammonia,  and  sulphureted  hydrogen.  The  tar  and  ammonia 
are  condensed  and  removed.  The  gas  also  undergoes  puri¬ 
fication  and  scrubbing ;  in  the  former  process,  the  gas  is  forced 
in  thin  streams  through  pans  filled  with  lime,  oxide  of  iron, 
etc.;  and  in  the  latter,  through  bodies  of  liquid  charged  with 
certain  chemicals. 

Oil  gas  is  made  from  petroleum  in  a  similar  way  and 
from  almost  any  kind  of  oil,  grease,  or  fat. 

Producer  gas  differs  from  the  coal  gas  commonly  used  for 
lighting,  in  having  much  less  combustible  matter,  and  in 
having  a  large  percentage  of  nitrogen.  It  is  made  by  burning 
anthracite  or  bituminous  coal  in  a  closed  furnace,  with  a 
supply  of  air  too  small  for  complete  combustion.  The  average 
quality  of  producer  gas  contains  from  10  to  15  per  cent,  of 
hydrogen,  from  20  to  30  per  cent,  of  carbon  monoxide  ( CO), 
and  from  40  to  60  per  cent,  of  nitrogen.  Producer  gas  burns 
with  a  dull  reddish  flame,  and  its  heating  value  is  about  one- 
fourth  that  of  good  coal  gas. 

Water  gas  is  made  from  anthracite  coal  and  steam.  The 
coal  is  placed  in  an  air-tight  cylinder,  ignited,  and  raised  to 
an  incandescent  heat  by  an  air  blast ;  the  blast  is  then  shut 
off,  and  dry  steam  is  blown  through  the  glowing  fuel.  The 
intense  heat  breaks  up  the  steam  into  free  oxygen  and  hydro¬ 
gen.  the  oxygen  combining  with  the  hot  carbon,  forming 
CO,  and  the  hydrogen  passing  along  with  it,  but  not  com¬ 
bining.  These  are  then  led  to  a  gas  holder.  The  operations 
of  blowing  up  and  making  gas  alternate  at  intervals  of  about 


GAS. 


319 


3  minutes,  until  the  fuel  is  exhausted.  The  fresh  gas  burns 
perfectly  in  heating  burners,  but  when  used  for  lighting  pur¬ 
poses,  is  always  enriched  in  carbon,  by  the  vaporization  of 
petroleum  before  it  leaves  the  generator.  The  density  of 
pure  water  gas  is  .4  that  of  air.  It  naturally  has  very  little 
odor,  but  some  impurities  are  allowed  to  remain  to  give  the 
gas  a  perceptible  odor. 

Acetylene  (chemical  symbol,  C2-H2)  is  composed  of  12  parts 
of  carbon  to  1  of  hydrogen  by  weight,  or  92.3  per  cent,  carbon 
and  7.7  per  cent,  hydrogen.  It  is  the  most  brilliant  illumi¬ 
nating  gas  known.  Its  density  is  about  .91,  and  its  weight  at 
32°  F.  is  .073  lb.  per  cu.  ft.  It  is  without  color,  and  has  a 
strong  odor,  like  garlic.  It  is  poisonous  to  breathe,  in  about 
the  same  degree  as  ordinary  gas.  The  heat  developed  by  the 
combustion  of  1  cu.  ft.  is  theoretically  1,090  heat  units. 
Acetylene  is  manufactured  by  mixing  calcium  carbide  with 
water.  The  carbide  is  a  mixture  of  coke  and  lime  which 
had  been  fused  in  an  electric  furnace.  It  is  reddish  brown, 
or  gray,  in  color,  somewhat  crystalline,  and  decomposes  water 
like  ordinary  quicklime ;  the  calcium  takes  oxygen  from  the 
water,  forming  oxide  of  calcium,  or  common  quicklime, 
while  the  carbon  combines  with  the  hydrogen  of  the  water, 
and  forms  the  desired  compound,  acetylene.  Considerable 
heat  is  given  off  during  the  operation. 

Pure  carbide  of  calcium  will  yield  5.4  cu.  ft.  of  acetylene 
per  pound  ;  but  it  is  hardly  safe  to  reckon  upon  more  than  4.5 
cu.  ft.  from  the  commercial  carbide.  Special  burners  are 
required  for  acetylene  illumination,  provided  with  small  air 
holes  to  supply  more  air  to  the  flame  than  is  obtained  by 
ordinary  burners.  Acetylene  will  give  a  light  of  about  24 0 
candlepower  when  burned  at  the  rate  of  5  cu.  ft.  per  hoiir, 
while  good  coal  gas  only  gives  16  candlepower  at  the  same 
rate  of  combustion.  Acetylene  can  be  reduced  to  liquid 
form,  at  a  temperature  of  60°,  by  a  pressure  of  about  oOO  lb. 
per  sq.  in.,  but  is  then  unsuitable  for  use  in  buildings,  owing 
to  the  danger  of  explosion.  Acetylene  corrodes  silver  and 
copper,  forming  explosive  compounds,  but  does  not  affect 
brass,  iron,  lead,  tin,  or  zinc.  These  facts  should  be  borne  in 
mind  when  constructing  apparatus  for  its  use. 


320 


GAS  AND  GAS- FITTING. 


Gasoline  gas,  or  carbureted  air,  sometimes  called  air  gas, 
is  a  mixture  of  gasoline  vapor  with  air,  and,  when  pure,  is  so 
rich  in  carbon  that  special  burners  must  be  employed  for 
lighting  purposes.  The  quantity  required  to  produce  1,000 
cu.  ft.  of  gas  of  from  14  to  16  candlepower  is  about  gal. 
of  the  best  grade,  and  more  if  the  gasoline  is  of  a  lower  grade. 
The  specific  gravity  of  gasoline  is  about  .74  that  of  water. 
The  temperature  of  a  gasoline-gas  machine  should  range 
between  40°  to  80°.  The  highest  grade  of  gasoline,  that  is, 
the  grade  that  will  evaporate  most  freely  at  ordinary  tem¬ 
peratures,  should  be  used  for  winter  service.  The  generators 
should  be  located  outside  the  building,  in  a  sheltered  place. 
An  air  pump  is  used  to  pump  fresh  air  through  the  gen¬ 
erator,  and  a  mixing  device  is  commonly  employed  for  mixing 
air  with  the  gas  before  it  reaches  the  burners.  The  pump  and 
mixer  are  usually  located  in  the  cellar  of  the  building. 


PRESSURE  OF  GAS. 

If  a  gas  is  lighter  than  air,  at  the  same  temperature,  the 
pressure  will  be  greatest  at  the  top  of  the  chamber  containing 
the  gas ;  if  heavier,  the  greatest  pressure  will  be  at  the  bottom 
of  the  chamber.  The  upward  pressure  of  gas  having  a  less 
density  than  air  is  caused  by  its  deficiency  in  weight,  and  con¬ 
sequent  inability  to  balance  the  pressure  of  the  atmosphere. 

For  illustration,  consider  a  column  of  gas  1  ft.  square 
and  100  ft.  high,  having  a  density  of  .5,  or  one-half  that  of 
air,  the  temperature  being  the  same  as  that  of  the  atmos¬ 
phere — say  60°.  Air  at  60°  weighs  .0764  lb.  per  cu.  ft.,  and  as 
the  column  contains  100  cu.  ft.,  it  will  weigh  .0764  X  100 
=  7.64  lb.  The  gas  having  a  density  of  .5  will  weigh  only 
half  as  much,  or  3.82  lb.,  and  is,  therefore,  unable  to  balance 
an  equal  volume  of  air.  Consequently,  it  is  pressed  upwards 
with  a  force  of  7.64  —  3.82  =  3.82  lb.  against  the  top  of  the 
chamber  which  contains  it.  Whatever  the  actual  pressure  of 
the  gas  may  be  at  the  bottom  of  the  column,  it  will,  in  this 
case,  be  increased  at  the  top  to  the  extent  of  3.82  lb.  per  sq.  ft. 

The  increase  of  pressure  in  each  10  ft.  of  rise  in  the  pipes, 
with  gas  of  various  densities,  is  shown  ir>  the  following  table: 


GAS. 


321 


Rise  in  pressure  (in. 
of  water) . 

0. 

.0147 

.0293 

.044 

.058 

.073 

.088 

.102 

Density  of  gas . 

1. 

.9 

.8 

.7 

.6 

.5 

.4 

.3 

Example. — The  pressure  in  the  basement,  at  the  meter,  is 
1.2  in.  of  water ;  what  Avill  be  the  pressure  on  the  sixth  story, 
70  ft.  above,  the  density  of  the  gas  being  .4? 

Solution.— The  table  shows  that  the  increase  will  be  .088 
for  each  10  ft.  of  rise ;  therefore,  .088  X  7  =  .616  increase. 
Then  pressure  at  sixth  story  =  1.2  +  .616  =  1.816  in. 


MEASUREMENT  OF  PRESSURE  AND  FLOW. 

Pressure.— The  pressure  of  gas  is  measured  by  the  common 
water  gauge,  which  is  shown  in  Fig.  16.  The 
tubes  b  and  c  are  glass,  and  are  filled  with 
water  up  to  the  zero  of  the  scale,  which  is 
graduated  in  inches  and  fifths  or  tenths  of  an 
inch.  The  tube  c  is  opened  to  the  air  at  the 
top.  When  pressure  is  admitted  to  a,  the 
water  will  sink  in  the  tube  6,  and  will  rise 
in  c.  The  difference  in  the  height  of  the 
water  in  the  two  tubes,  measured  in  inches, 
is  the  measure  of  the  pressure  exerted  in 
inches  of  water.  For  measuring  heavier  pres¬ 
sures,  mercury  is  used  instead  of  water. 

Pressures  measured  in  inches  of  water  or 
mercury  may  be  translated  into  pounds  per 
square  inch  or  square  foot,  by  multiplying 
the  reading  by  the  following  figures : 

1  in.  of  water  at  62°  F.  =  5.2020  lb.  per  sq.  ft. 

1  in.  of  water  at  62°  F.  =  .0362  lb.  per  sq.  in. 

1  in.  of  mercury  62°  F.  =  .4897  lb.  per  sq.  in. 

Pressure  per  square  inch  or  square  foot 
may  be  converted  into  inches  or  feet  of 
water,  or  inches  of  mercury,  by  multiplying  the  pressures  by 
the  following  figures : 

1  lb.  per  sq.  ft.  =  .1923  in.  of  water  at  62°  F. 

1  lb.  per  sq.  in.  =  27.70  in.  of  water  at  62°  F. 

1  lb.  per  sq.  in.  =  .2042  in.  of  mercury  at  62°  F. 


Fig.  16. 


322 


GAS  AND  GAS-FITTING. 


gas,  passing  through  a  pipe  in  a 
given  time,  is  computed  by  multi¬ 
plying  the  velocity  by  the  area  of 
the  pipe.  The  velocity  may  be 
measured  by  a  Pitot  tube,  as  shown 
in  Fig.  17.  This  consists  of  two 
tubes,  a  and  b ,  inserted  in  a  plug  c, 
the  lower  end  of  a  being  square, 
and  that  of  b  curved  to  face  the 
current ;  the  upper  ends  are  con¬ 
nected  to  a  water  gauge  d.  Gas 
entering  through  b  depresses  the 
water  column  as  shown  ;  the  veloc¬ 
ity  corresponding  to  the  reading  is 
found  from  tables  which  are  gen¬ 
erally  furnished  with  the  instrument. 

The  actual  quantity  of  the  gas  is  computed  by  correcting 
the  volume  for  temperature  and  pressure,  reducing  it  to  a 
volume  at  standard  temperature  of  32°  F.  and  standard 
pressure  of  1  in.  of  water.  The  correction  for  temperature 
may  be  made  as  follows  : 

Rule  I. — Multiply  the  measured  volume  by  192  and  divide  the 
product  by  h&O  plus  the  actual  temperature.  The  quotient  will  be 
the  volume  at  82°  F. 

The  correction  for  pressure  may  be  made  as  follows  : 

Rule  2. — Multiply  the  volume  at  82°  F.  by  the  pressure  in  inches 
of  water  plus  107,  and  divide  the  product  by  4 08.  The  quotient 
will  be  the  volume  at  1  inch  pressure,  and  at  32°  F. 

Example.— A  pipe  passes  1,000  cu.  ft.  of  gas  per  hour,  under 
a  pressure  of  8  in.  of  wrater  and  at  a  temperature  of  60°.  What 
will  the  volume  be  when  the  pressure  is  reduced  to  1  in.,  and 
the  temperature  to  32°  ? 

Solution.— By  the  first  rule,  the  volume  at  32°  is 


Flow.— The  volume  of 


1,000  X  492 


=  946.1  cu.  ft. 


460  +  60 

By  rule  2,  the  volume  under  1  in.  pressure  and  at  32°  is 
946.1  X  (8 +  407) 


408 


962.3  cu.  ft. 


If  the  quantity  of  gas  delivered  through  a  pipe  of  given 


GAS. 


323 


length  is  known,  that  supplied  through  a  longer  or  shorter 
pipe  is  to  the  known  volume  as  the  square  root  of  the  given 
length  is  to  the  square  root  of  the  required  length.  With  pipes 
of  the  same  length  and  diameter,  the  volumes  delivered  at 
any  proposed  pressure  is  to  that  supplied  at  any  other  pressure 
as  the  square  root  of  the  proposed  pressure  is  to  the  square 
root  of  the  given  pressure. 


GAS  METERS  AND  PRESSURE  REGULATORS. 

Meters. — For  ordinary  purposes,  the  volume  of  gas  passing 
through  a  pipe  is  measured  by  an  apparatus  called  a  gas  meter. 
A  gas  meter  measures  the  volume  only,  and  its  indications 
are  not  affected  by  any  change  that  may  occur  in  the  pres¬ 
sure  of  the  gas.  The  difficulty  thus  encountered  in  correctly 
measuring  the  volume  of  gas  actually  delivered  under  varying 
pressures,  is  overcome  by  using  a  governor  between  the  meter 
and  the  street  main,  or  service  pipe.  The  governor  is  a  species 
of  reducing  valve  which  will  receive  gas  at  any  pressure, 
whether  steady  or  variable,  and  will  discharge  it  at  a  steady 
low  pressure. 

Fig.  18  shows  a  meter  of  the  ordinary  type.  To  read 


such  a  meter,  note  the  lesser  of  the  two  figures  between  which 
each  hand  points,  or  the  figure  to  which  it  points,  beginning 
at  the  left-hand  dial ;  then  add  two  ciphers  to  the  right  of 
the  three  figures,  and  the  number  so  obtained  will  be  the 


324 


GAS  AND  GAS-FITTING. 


amount  of  gas  in  cubic  feet  which  the  meter  has  measured. 
Thus  the  pointers  in  the  diagram  indicate  that  14,200  cu.  ft. 
of  gas  have  passed  through  the  meter. 

The  dial  marked  two  feet  may  he  used  to  ascertain  the  quan¬ 
tity  of  gas  consumed  per  hour  by  a  burner,  by  noting  the 
time  required  for  the  pointer  to  make  a  revolution.  Thus, 
the  hand  will  make  revolutions  per  hour  if  5  cu.  ft.  pass 
through  the  meter  in  that  time.  This  dial  may  also  be  used 
in  testing  for  leaks. 

Pressure  Regulators.— The  objects  sought  in  the  use  of  pres¬ 
sure  regulators  or  governors  are  economy  in  the  consumption 
of  gas,  steadiness  of  the  lights,  and  most  effective  opera¬ 
tion  of  the  burners.  It  is  of  great  importance  that  both 
volume  and  pressure  at  the  burners  should  be  closely  regu¬ 
lated.  The  amount  of  gas  wasted  by  over  pressure  is  much 
greater  than  is  generally  believed.  A  good  new  lava-tip 
burner  consuming  5  cu.  ft.  per  hour  at  .5  in.  pressure,  will 
consume  about  .5  of  a  cu.  ft.  more  for  each  increase  of  .1  in. 
in  the  pressure.  Thus  an  over  pressure  of  .1  in.  will  increase 
the  gas  bill  about  10  per  cent.  The  variation,  in  even  the 
best  regulated  systems,  is  usually  much  greater  than  one- 
tenth  inch,  and  is  freciuently  ten-tenths  or  more. 

The  two  systems  ot  regulation  in  use  are  the  pressure  and 
the  volumetric  regulation.  In  the  first  system,  a  governor  is 
attached  to  the  service  pipe  at.  the  meter,  and  the  house  dis¬ 
tributing  pipes  are  maintained  at  constant  pressure ;  in  the 
second  system,  each  burner  is  supplied  with  a  governor,  the 
pressure  in  the  pipes  not  being  controlled. 

The  proper  place  for  a  pressure  regulator,  if  used,  is  between 
the  meter  and  the  main.  The  meter  should  then  be  adjusted 
to  suit  the  house  pressure  instead  of  the  street  pressure. 

The  pressure  required  at  the  burners,  to  secure  the  best 
results,  varies  greatly  in  different  forms  of  apparatus.  The 
following  are  the  pressures  generally  used : 


Argand  burners . . 2  in.  of  water. 

Common  batswing  burners . . .  .5  in.  of  water. 

Wellsbach  incandescent  burners . 5  or  more. 

Wenham  and  Lebrun  lamps  . 5  to  1  or  more. 

Atmospheric  burners . 1.0  or  more. 


6 AS-FITTING. 


325 


i 


GAS-FITTING. 


ILLUMINATION  REQUIRED. 

The  number  of  gas  lights  required  to  properly  illuminate 
a  room  depends  on  its  size,  condition  of  wall  surfaces,  etc. 
The  reflection  from  the  walls  in  small  rooms  is  proportion¬ 
ately  greater  than  in  large  ones,  and  hence  a  less  number 
of  burners  is  required  in  proportion  to  the  floor  space.  A 
5'  (cubic  feet  per  hour)  batswing  burner  is  assumed  to  give 
a  light  of  16  candlepower  under  a  pressure  of  .5  in.  of  water. 

For  large  rooms,  such  as  a  church,  etc.,  the  proper  illumi¬ 
nation  will  be  furnished  by  using  one  burner  to  each  4  0  sq.ft, 
of  floor.  If  there  are  balconies,  etc.,  extra  lights  must  be 
provided  according  to  the  same  rule.  For  smaller  rooms, 
such  as  are  found  in  ordinary  dwellings,  the  proportion  may 
be  1  light  to  about  80  sq.  ft.  of  floor.  The  amount  of  light 
required  is,  therefore,  from  .4  to  .2  candlepower  per  square 
foot,  according  to  the  size  of  the  room. 

If  incandescent  gas  lights,  such  as  the  Welsbach,  are  used, 
the  number  of  lights  may  be  much  less,  as  these  lights  furnish 
from  50  to  60  candlepower  on  a  consumption  of  about  3  cu.  ft. 
of  gas  per  hour,  at  a  pressure  of  .5  in. 


SIZE  OF  PIPES. 

Each  pipe  must  have  enough  capacity  to  suppl\  all  its 
burners  when  they  are  in  full  operation.  Allowance  must 
also  be  made  for  all  heating  and  cooking  apparatus  likely  to 
be  required.  The  quantity  required  for  lighting  may  be 
reckoned  as  5  cu.  ft.  per  hour  for  each  burner,  unless  other¬ 
wise  given.  The  actual  quantity  required  by  improved 
burners,  however,  differs  so  much  that  it  is  impracticable  to 
compute  the  volume  required  by  merely  noting  the  number 

of  burners.  .  , 

Service  pipes  should  never  be  less  than  f  m.  because  of 

liability  to  chokage,  and,  if  of  iron,  it  is  advisable  to  make 
the  diameter  at  least  1  in.  For  small  cook  stoves,  the  supply 
pipe  should  be  at  least  i  in.,  and  for  larger  stoves,  1  to  1*  m. 


326 


GAS  AND  GAS-FITTING. 


Having  ascertained  the  probable  maximum  quantity 
required  in  cubic  feet  per  hour,  the  diameter  of  the  pipe  can 
be  round  from  the  following  table.  If  the  length  of  the  pro¬ 
posed  pipe  exceeds  the  maximum  length  given,  the  next 
larger  size  pipe  should  be  chosen.  If  the  pressure  exceeds 
2  in.,  the  principal  pipes  may  be  reduced  one  size.  If  the 
pressure  is  less  than  1  in.,  all  pipes  must  be  increased  one 
size,  and  with  very  long  pipes,  the  diameter  will  require  to  be 
increased  still  more.  When  gasoline  gas  is  used,  no  dis¬ 
tributing  pipe  should  be  less  than  |  in. 

Capacity  op  Gas  Pipes. 


Diameter 
of  Pipe. 

In. 

Maximum 

Length. 

Ft. 

Capacity  per  Hour. 

Coal  Gas. 

Cu.  Ft. 

Gasoline  Gas. 
Cu.  Ft. 

JL 

6 

10 

8 

20 

15 

10 

30 

30 

20 

t 

50 

100 

75 

1 

70 

175 

125 

H 

100 

300 

200 

H 

150 

500 

350 

2 

200 

1,000 

700 

2? 

300 

1,500 

1,100 

3 

450 

2,250 

1,500 

4 

600 

3,750 

2,500 

In  this  table,  the  pressure  is  assumed  to  be  about  2  in.  of 
water.  The  quantities  stated  are  those  which  the  pipes  will 
deliver  at  the  burners  without  objectionable  fall  of  pressure. 


INSTALLATION  AND  TESTING. 

The  pipes  used  for  the  distribution  of  gas  in  buildings  are 
standard  plain  wrought-iron  or  steel  pipe. 

If  the  location  of  the  pipes  is  not  shown  by  the  architect, 
then  the  gas-fitter  must  use  his  own  judgment  in  determining 
their  position.  He  should  be  governed  by  the  following  con¬ 
siderations  ; 


GAS-FITTING. 


327 


1.  The  pipes  should  run  io  the  fixtures  in  the  most  direct 
manner  practicable. 

2.  The  pipes  must  be  graded  to  secure  proper  drainage  with¬ 
out  excessive  cutting  of  fioorbeams,  or  otherwise  damaging 
the  building. 

3.  Pipes  which  run  crossways  of  fioorbeams  should  be  laid 
not  more  than  1  ft.  from  the  wall,  to  avoid  serious  injury  to 
the  floor. 

4.  Fixtures  should  be  supplied  by  risers  rather  than  by 
drop  pipes,  as  far  as  practicable. 

5.  All  pipes  should  be  located  where  they  can  be  got  at  for 
repairs,  with  the  least  possible  damage  to  the  floors  or  walls. 

6.  The  fittings  should  be  malleable  iron  galvanized,  beaded 
fittings  being  preferable  to  plain  ones.  Plain  black  iron  fit¬ 
tings  should  never  be  used  on  important  work. 

Testing. — As  soon  as  the  pipes  are  all  in  place  and  are 
properly  secured,  the  system  should  be  tested  to  find  if  it  is 
gas-tight.  Air  should  be  forced  in  the  system  until  the  gauge 
indicates  15  or  20  in.  of  mercury,  or  7  to  10  lb.  per  sq.  in.,  the 
pressure  being  continued  for  about  an  hour,  and  if  the  gauge 
shows  a  falling  off  in  pressure  of  more  than  i  in.  of  mercury, 
or  |  lb.  per  sq.  in.,  then  the  system  cannot  be  passed  as  perfect. 
The  mercury-column  differential  proving  gauge  is  well 
adapted  for  testing  gas  pipes,  etc.,  which  are  to  be  made 
air-tight ;  common  spring  gauges  are  unreliable. 

The  extent  of  a  leak  may  be  judged  by  the  rapidity  of  the 
fall  in  pressure,  but  its  location  must  be  found  by  the  sense  of 
smell.  For  this  purpose  a  small  quantity  of  ether  should  be 
introduced  into  the  pipes.  The  vapor  of  the  ether  will  diffuse 
throughout  the  system  and  escape  from  the  leak,  where  it  will 
be  detected  by  its  odor.  The  gauge  should  be  provided  with 
an  ether  cup  especially  for  testing  purposes. 

In  case  of  large  buildings,  it  is  ad  visible  to  test  the  piping 
in  sections,  say  one  floor  at  a  time,  because  it  is  much  easier 
to  locate  leaks.  After  each  section  is  tested  they  may  be  con¬ 
nected,  and  then  subjected  to  a  final  test. 

The  pipes  should  not  be  covered  until  the  tests  are  com¬ 
pleted.  The  owner,  architect,  or  inspector  should  witness  the 
tests. 


328 


ESTIMATING. 


ESTIMATING. 


APPROXIMATE  ESTIMATES. 

The  following  table  shows  the  approximate  cost  per  cubic 
foot  of  various  kinds  of  structures.  In  computing  the  con¬ 
tents  of  a  building  there  is  no  uniformity  in  practice,  but  no 
great  error  will  be  made  in  figuring  the  solid  contents  from 
floor  of  cellar  to  ridge  of  roof. 

Cost  of  Buildings  per  Cubic  Foot. 


Class  of  Building. 

Cost  per  Cu.  Ft. 
Cents. 

Small  frame  buildings,  costing  from  $800  to 
$1,500  . 

8  to  9 

Frame  houses,  8  to  12  rooms,  costing  from 
$1,500  to  $10,000 . 

9  to  11 

Brick  houses,  8  to»10  rooms . 

10  to  14 

Highly  finished  city  dwellings  (brick  or 
stone) . 

17  to  20 

Schoolhouses  (brick) . 

9  to  11 

Churches  (stone) . 

20  to  25 

Office  buildings  (well  finished) . 

30  to  40 

Hospitals,  libraries,  and  hotels . 

32  to  44 

STONEWORK. 

Stone  masonry  is  usually  measured  by  the  perch  ;  in  some 
sections  of  the  country,  however,  measurement  by  the  cord  is 
preferred,  but  the  best  method  (as  being  invariable)  is  by  the 
cubic  yard.  In  estimating  by  the  perch,  it  should  be  stated 
how  much  the  perch  is  taken  at,  whether  24f  or  25  cu.  ft. 
Note  should  also  be  made  in  regard  to  deduction  for  open¬ 
ings,  as  in  most  localities  it  is  not  customary  to  deduct  those 
under  a  certain  size,  and  corners  are  usually  measured  twice. 

Rough  stone  from  the  quarry  is  usually  sold  under  two 
classifications,  namely,  rubble  and  dimension  stone.  Rubble 
consists  of  pieces  of  irregular  size,  such  as  are  most  easily 
obtained  from  the  quarry,  up  to  12  in.  in  thickness  by  24  in. 


STONE  WORK. 


329 


in  length.  Stone  ordered  of  a  certain  size,  or  to  square  over 
24  in.  each  way  and  to  be  of  a  particular  thickness,  is  called 
dimension  stone. 

Rubble  masonry  and  stone  backing  are  generally  figured 
by  the  perch  or  the  cubic  yard.  Dimension-stone  footings 
are  measured  by  the  square  foot  unless  they  are  built  of  large 
irregular  stone,  in  which  case  they  are  measured  the  same  as 
rubble.  Ashlar  work  is  always  figured  by  the  superficial 
foot ;  openings  are  usually  deducted  and  the  jambs  are  meas¬ 
ured  in  with  the  face  work.  Flagging  and  slabs  of  all  kinds, 
such  as  hearths,  treads  for  steps,  etc.,  are  measured  by  the 
square  foot ;  sills,  lintels,  moldings,  belt  courses,  and  cor¬ 
nices,  by  the  lineal  foot,  and  irregular  pieces  are  generally 
figured  by  the  cubic  foot.  All  carved  work  is  done  at  an 
agreed  price  by  the  piece. 


METHODS  OF  ESTIMATING  MASONRY. 

The  following  proportions  and  cost  of  materials,  and 
amount  of  labor  required  for  the  classes  of  work  below  speci¬ 
fied,  are  reasonably  accurate,  and  will  serve  to  give  a  good 
idea  of  how  to  estimate  such  work. 

Cost  of  Rubble  Masonry  per  Perch. 


Using  l-to-3  Lime  Mortar. 

1  perch  stone  (25  cu.  ft.)  delivered  at  work . $1.25 

1  bu.  lime . 25 

£  load  of  sand,  at  $1.50  per  load . . . .  .25 

l  day  mason’s  labor,  at  $2.50  per  day . 83 

i  day  helper’s  labor,  at  $1.50  per  day . 38 


Total .  $2.96 

Using  l-to-3  Portland  Cement  Mortar. 

1  perch  stone . $1.25 

i  bbl.  Portland  cement,  at  $2.60  per  bbl .  1.30 

£  load  sand,  at  $1.50  per  load  . 25 

i  day  mason’s  labor,  at  $2.50  per  day . 83 

|  day  helper’s  labor,  at  $1.50  per  day . 38 


Total  . . .  $*-01 


330 


ESTIMATING. 


Using  l-to-3  Rosendale  Cement  Mortar. 

1  perch  stone . . .  $1.25 

h  bbl.  Rosendale  cement,  at  $1.25  per  bbl . 63 

l  load  sand,  at  $1.50  per  load . 25 

|  day  mason’s  labor,  at  $2.50  per  day  . 83 

y  day  helper’s  labor,  at  $1.50  per  day . 38 


Total  . $3.34 

Cost  of  1  Square  Foot  of  Ashlar. 

\ 

Cost  of  stone,  bluestone  facing . $  .30 

Hauling  stone,  say  TV  of  cost  of  stone . 03 

Mortar  . 01 

Labor,  estimating  80  sq.  ft.  per  day  for  two  masons  and 
one  laborer : 

2  masons,  at  $3.00  per  day . 08 

1  laborer,  at  $1.50  per  day . 02 


Cost  per  square  foot . $  .44 

Cost  of  1  Cubic  Yard  of  Concrete. 

1  bbl.  of  Rosendale  cement,  at  $1.25  per  bbl .  $1.25 

3  bbl.  of  sand,  or  |  load,  at  $1.50  per  load . 50 

1  cu.  yd.  (about  6  bbl. )  of  broken  stone,  at  $1.50  per  cu.yd.  1.50 

Mason,  i  day,  at  $2.50 . 63 

Laborer,  1  day,  at  $1.50 .  1.50 


Total . $5.38 

Cost  of  1  Square  Yard  of  Cellar  Floor. 

Concrete,  in.  thick,  at  $5.38  per  cu.  yd . $  .67 

Sand  bed,  6  in.  thick,  approximately  1  bbl . 17 

Spreading  sand .  .02 

fy  bbl.  of  Portland  cement  for  finishing  coat,  at 

$2.60  per  bbl . 22 

rV  bbl.  of  white  sand,  at  $1.00  per  bbl . .08 

Mixing  and  spreading  surface  layer . 08 


Cost  per  square  yard . . . $1.24 


STONEWORK. 


331 


DATA  ON  ASHLAR  AND  CUT  STONE. 

Cost. — The  following  figures  are  average  prices  of  stone 
when  the  transportation  charges  are  not  excessive;  the 
figures  are  not  given  as  fixed  values,  but  to  show  the  relative 
costs.  They  are  based  on  quarrymen’s  wages  of  $2.25  per 
day,  and  stone  cutters’  of  $3.00  per  day. 

First-class  rock-face  bluestone  ashlar,  with  from  6"  to  10" 
beds,  dressed  about  3  in.  from  face,  will  cost,  ready  for  lay 
ing,  from  35  to  45  cents  per  square  foot,  face  measure ;  while 
very  good  work  will  cost  from  25  to  40  cents  per  square  foot. 
Regular  coursed  bluestone  ashlar,  12  to  18  in.  high,  with  from 
8"  to  12"  beds,  will  cost  about  50  cents  per  square  foot.  To 
this  (and  the  previous  figures)  must  be  added  the  cost  of 
hauling,  wrhich  on  an  average  will  be  about  2  cents  per  square 
foot.  The  cost  of  setting  ashlar  may  be  taken  at  about  10 
cents  per  square  foot. 

The  rough  stock  for  dimension  stone  will  cost,  at  (lie 
quarry,  if  Quincy  granite,  in  pieces  of  a  cubic  yard,  or  less, 
from  50  to  75  cents  per  cubic  foot ;  if  bluestone,  about  50  cents ; 
if  Ohio  sandstone,  about  30  cents  per  cubic  foot;  if  Indiana 
limestone,  about  25  cents  per  cubic  foot ;  and  if  Lake  Superior 
red  stone,  about  40  cents  per  cubic  foot. 

Flagstones  for  sidewalks,  ordinary  stock,  natural  surface, 
3  in.  thick,  with  joints  pitched  to  line,  in  lengths  (along 
walk)  from  3  to  5  ft.,  will  cost,  for  3'  walk,  about  8  cents  per 
square  foot  (if  2  in.  thick.  6  cents);  for  4'  walk,  9  cents;  and 
for  5'  walk,  10  cents  per  square  foot.  The  cost  of  laying  all 
sizes  will  average  about  3  cents  per  square  foot.  The  above 
figures  do  not  include  cost  of  hauling. 

Curbing  (4"  X  24"  granite)  will  cost,  at  quarry,  from  25  to 
30  cents  per  lineal  foot ;  digging  and  setting  will  cost  from  10 
to  12  cents  additional ;  and  the  cost  of  freight  and  hauling 
must  also  be  added. 

The  following  figures  show  the  approximate  cost  of  cut 
bluestone  for  various  uses : 

Flagstone,  5",  size  8  ft.  X  10  ft.,  edges  and  top  bush- 

hammered,  per  sq.  ft.,  face  measure  . $  -65 

Flagstone,  4",  size  5  ft.  X  5  ft.,  select  stock,  edges  clean 
cut,  natural  top,  per  sq.  ft . 


.30 


332 


ESTIMATING. 


Door  sills,  8  in.  x  12  in.,  clean  cut,  per  lineal  foot . $1.25 

Window  sills,  5  in.  V  12  in.,  clean  cut,  per  lineal  foot . 80 

Window  sills,  4  in.  X  8  in.,  clean  cut,  per  lineal  foot . .  .45 

Window  sills,  5  in.  X  8  in.,  clean  cut,  per  lineal  foot . 60 

Lintels,  4  in.  X  10  in.,  clean  cut,  per  lineal  foot . _  .60 

Lintels,  8  in.  X  12  in.,  clean  cut,  per  lineal  foot .  1.10 

Water-table,  8  in.  X  12  in.,  clean  cut,  per  lineal  foot .  1.25 

Coping,  4  in.  X  21  in.,  clean  cut,  per  lineal  foot .  1.10 

Coping,  4  in.  X  21  in.,  rock-face  edges  and  top,  per  lin.  ft.  .45 
Coping,  3  in.  x  15  in.,  rock- face  edges  and  top,  per  lin.  ft.  .25 
Coping,  3  in.  X 18  in.,  rock-face  edges  and  top,  per  lin.  ft.  .30 

Steps,  sawed  stock,  7  in.  X  14  in.,  per  lineal  foot . 90 

Platform,  6  in.  thick,  per  square  foot . 45 


To  the  prices  of  cut  stone  above  given  must  be  added  the 
cost  of  setting,  which,  for  water-tables,  steps,  etc.,  will  be 
about  10  cents  per  lineal  foot,  and,  for  window  sills,  etc., 
about  5  cents  per  lineal  foot.  In  addition,  allow  about  10 
cents  per  cubic  foot  for  fitting,  and  about  5  cents  per  cubic 
foot  for  trimming  the  joints  after  the  pieces  are  set  in  place. 

A  stone  cutter  can  cut  about  6  sq.  ft.  of  granite  per  day, 
8  sq.  ft.  of  bluestone,  and  about  10  sq.  ft.  of  Ohio  sandstone  or 
Indiana  limestone.  These  figures  are  for  8-cut  patent- 
hammered  work.  For  rock-face  ashlar  (beds  worked  about 
3  in.  from  face,  the  rest  pitched),  a  workman  can  dress  from 
25  to  28  sq.  ft.  of  random  ashlar  per  day,  and  from  18  to  20  sq.  ft. 
of  coursed  ashlar.  In  dressing  laminated  stone,  from  2  to  3 
times  more  work  in  a  day  can  be  done  on  the  natural  surface 
than  on  the  edge  of  layers.  In  figuring  cut  stone,  an  ample 
allowance  should  be  made  for  waste,  which,  on  an  average, 
will  be  25  per  cent. 


BRICKWORK. 

Brickwork  is  generally  estimated  by  the  thousand  brick 
laid  in  the  wall,  but  measurements  by  the  cubic  yard  and  by 
the  perch  are  also  used.  The  following  data  will  be  useful 
in  calculating  the  number  of  brick  in  a  wall.  For  each 
superficial  foot  of  wall,  4  in.  (the  width  of  1  brick)  in  thick¬ 
ness,  allow  7h  brick ;  for  a  9"  (the  width  of  2  brick)  wall, 


BRICKWORK. 


333 


allow  15  brick;  for  a  13"  (the  width  of  3  brick)  wall,  allow 
22i  brick  ;  and  so  on,  estimating  7j  brick  for  each  additional 

4  in.  in  thickness  of  wall.  The  above  figures  are  for  the 
ordinary  Eastern  standard  brick,  which  is  about  8£  X  4  X  2£  in. 
in  dimensions.  If  smaller  brick  are  used,  the  figures  will  be 
increased  proportionately.  As  brick  vary  considerably,  a 
minimum  size  should  be  specified,  when  a  large  number  are 
bought ;  otherwise,  many  more  will  be  required  than  were 
figured  on.  If  brickwork  is  estimated  by  the  cubic  yard, 
allow  500  brick  to  a  yard.  This  figure  is  based  on  the  use  of 
the  size  of  brick  given  above,  with  mortar  joints  not  over  f  in. 
thick.  If  the  joints  are  |  in.  thick,  as  in  face  brickwork, 
1  cu.  yd.  will  require  about  575  brick.  Iu  making  calcula¬ 
tions  of  the  number  of  brick  required,  an  allowance  of,  say, 

5  per  cent,  should  be  made  for  waste  in  breakage,  etc. 

The  practice  in  regard  to  deductions  for  openings  is  not 
uniform  throughout  the  country,  but  small  openings  are 
usually  counted  solid,  as  the  cost  of  extra  labor  and  the  waste 
in  working  around  these  places  balances  that  of  the  brick¬ 
work  saved.  All  large  openings,  100  sq.  ft.  or  over  in  area, 
should  be  deducted. 

When  openings  are  measured  solid,  it  is  not  usual  to  allow 
extra  compensation  for  arches,  pilasters,  corbels,  etc.  Rubbed 
and  ornamental  brickwork  should  be  measured  separately, 
and  charged  for  at  a  special  rate. 

Brick  footings  may  be  computed  by  the  lineal  foot.  The 
following  table,  based  on  steps  or  offsets  of  one-quarter  brick, 
or  2  in.,  for  each  course  in  the  footing,  gives  the  number  of 
brick  per  lineal  foot  in  footings  for  brick  walls  from  9  to  2G  in. 
thick : 

9"  wall,  footing  2  courses,  10£.  18"  wall,  footing  4  courses,  39. 

13"  wall,  footing  3  courses,  22b  22"  wall,  footing  5  courses,  60. 

26"  wall,  footing  6  courses,  85£. 


DATA  ON  BRICKWORK. 

The  following  estimates  on  the  cost  of  brickwork  are  very 
carefully  compiled,  and  will  be  found  trustworthy.  It  is  to 
be  understood  that  the  prices  will  vary  with  the  cost  of 
materials  and  labor ;  but  the  proportions  will  be  constant. 


v 


384 


ESTIMATING. 


The  figures  are  based  on  kiln,  or  actual,  count— that  is,  with 
deductions  for  openings.  When  the  work  is  measured  with 
no  deductions  for  openings,  the  cost  per  thousand  may  be 
assumed  as  about  15  per  cent,  less  than  the  prices  given, 
which  are  exclusive  of  builder’s  profit. 

Cost  op  Common  Brickwork  per  Thousand  Brick. 

Using  l-to-8  Lime  Mortar. 

1,000  brick  . $  6.00 

3  bu.  lump  lime  at  $.25  per  bu . 75 

£  load  sand  (£  cubic  yard)  at  $1.50  per  load . 75 

7  hours,  bricklayer,  at  $.35  per  hour  .  2.45 

7  hours,  laborer,  at  $.15  per  hour . 1.05 

Total . $11.00 

Using  l-to-8  Portland  Cement  Mortar. 

1,000  brick  . . . $  6.00 

U  bbl.  Portland  cement,  at  $2.60  per  bbl .  3.90 

h  load  sand,  at  $1.50  per  load . 75 

7  hours,  bricklayer,  at  $.35  per  hour .  2.45 

7  hours,  laborer,  at  $.15  per  hour .  1.05 


Total . $14.15 

Using  1-to-U  Lime-and-  Cement  Mortar. 

1,000  brick . $  6.00 

3  bu.  lime,  at  $.25  per  bu . 75 

i  load  sand . 75 

1  bbl.  cement .  2.60 

7  hours,  bricklayer,  at  $.35  per  hour .  2.45 

7  hours,  laborer,  at  $.15  per  hour .  1.05 

Total . $13.60 

Using  l-to-8  Rosendale  Cement  Mortar. 

1,000  brick . . . $  6.00 

U  bbl.  Rosendale  cement,  at  $1.25  per  bbl .  1.87 

i  load  sand . 75 

7  hours,  bricklayer,  at  $.35  per  hour  .  2.45 

7  hours,  laborer,  at  $.15  per  hour .  1.05 

Total . $12.12 


CARPENTRY. 


335 


Cost  of  Pressed  Brickwork  per  Thousand  Brick. 
Using  Lime  Putty  Mortar. 

1.000  pressed  brick,  cost  from  $20.00  to  $40.00,  average  $30.00 


li  bu.  lime . 38 

£  load  fine  sand  . . 37 

30  hours,  bricklayer,  at  $.40  per  hour  . .  12.00 

15  hours,  laborer,  at  $.15  per  hour .  2.25 


Total . , . $45.00 


CARPENTRY. 


ESTIMATING  QUANTITIES. 


Board  Measure.— The  rough  lumber  used  in  framing  is  meas¬ 
ured  by  the  board  foot,  which  means  a  piece  12  in.  square  and 
1  in.  thick.  Lumber  is  always  sold  on  a  basis  of  1,000  feet 
board  measure;  the  customary  abbreviation  for  the  latter 
term  is  B.  M.,  and  for  thousand  is  M;  thus,  500  ft.  board 
measure,  costing  $14.00  per  thousand,  would  be  written:  500 
ft.  B.  M.  at  $14.00  per  M. 

To  obtain  the  number  of  board  feet  in  any  piece  of  timber, 
the  length  of  the  scantling  in  inches  may  be  multiplied  by 
the  end  area  in  sq.  in.,  and  the  result  divided  by  144.  For 
example,  the  number  of  feet  B.  M.  in  a  floor  joist  20  ft.  long, 
3  in.  thick,  and  10  in.  deep,  will  be  240  in.  (=  20  ft.  X  12) 
multiplied  by  30  sq.  in.  (the  end  area),  or  7,200  sq.  in.,  1  in. 
thick ;  dividing  by  144,  the  result  is  50  ft.  B.  M. 

The  rule  used  by  most  contractors  and  lumber  dealers  is  as 
follows :  Multiply  the  length  in  feet  by  the  thickness  and  width  in 
inches,  and  divide  the  product  by  12.  Thus,  a  scantling  26  ft. 
long,  2  in.  thick,  and  6  in.  wide,  contains 


26  ft.  B.  M. 


26  X  2  X  6 
12 

This  rule,  expressed  in  a  slightly  different  manner  more 
convenient  for  mental  computation,  is :  Divide  the  prod¬ 
uct  of  the  width  and  thickness  in  inches  by  12,  and  multiply  the 

quotient  by  the  length  in  feet.  Thus,  a  2"  X  10"  plank,  18  ft, 
o  v  1  o 

long,  contains  —  —  X  18  —  30  ft.  B.  M, 


336 


ESTIMATING. 


Studs.— To  calculate  the  number  of  studs,  set  on  16"  cen¬ 
ters,  the  following  rule  may  be  use# :  From  the  length  of  the 
partition  deduct  one-fourth,  and  to  this  result  add  1.  Count  the 
number  of  returns,  or  corners,  on  the  plan,  and  add  two  studs  for 
each  return.  (The  reason  for  adding  1  is  to  include  the  stud 
at  the  end,  which  would  otherwise  be  omitted.)  The  sills, 
plates,  and  double  studs  must  be  measured  separately. 

For  example,  the  total  number  of  studs  required  for  the 
lengths  of  partitions  given  at  the  left  is  as 
follows : 

Deducting  one-quarter  of  60  ft.  from  it,  the 


30  ft.  6  in. 
10  ft.  6  in. 
9  ft.  6  in. 
5  ft.  0  in. 
4  ft.  6  in. 

60  ft.  0  in. 


remainder  is  45;  adding  1  stud,  the  result  is 
46.  If  there  are,  say,  4  returns,  at  2  studs  each, 
the  total  number  is  46  +  8  =  54  studs. 

As  a  general  rule,  when  (as  is  usual j  the 
studs  are  set  at  16"  centers,  1  stud  for  each 
of  partition  will  be  a  sufficient  allowance  to 
plates,  and  double  studs.  Thus,  if  the  total 


foot  in  length 
include  sills, 

length  of  partitions  is  75  ft.,  75  studs  will  be  sufficient  for  sills, 
double  studs,  etc.  If  the  studs  are  set  at  12"  centers,  the  num¬ 
ber  required  will  be  equal  to  the  number  of  feet  in  length  of 
partition  plus  one-fourth.  Thus,  if  the  length  of  partitions 
is  72  ft.,  72  + 18,  or  90  studs,  will  include  those  required  for 
sills,  plates,  etc. 

The  same  rules  may  be  used  for  calculating  the  number  of 
joists,  rafters,  tie-beams,  etc. 

A  good  way  to  estimate  bridging  is  to  allow  2  cents  apiece, 
or  4  cents  a  pair  ;  this  will  be  sufficient  to  furnish  and  set  a 
pair  made  of  2"  X  3"  spruce  or  hemlock  stuff. 

Sheathing.— To  calculate  sheathing  or  rough  flooring  (which 
is  not  matched),  find  the  number  of  feet  B.  M.  required  to 
cover  the  surface,  making  no  deductions  for  door  or  window 
openings,  for  what  is  gained  in  openings  is  lost  in  w’aste.  If 
the  sheathing  is  laid  horizontally,  only  the  actual  measure¬ 
ment  is  necessary,  but,  if  it  is  laid  diagonally,  add  8  or  10  per 
cent,  to  the  actual  area. 

In  sheathing  roofs  where  many  hips,  valleys,  roof  dormers, 
etc.  occur,  there  will  be  a  great  deal  of  waste  material  caused 
by  mitering  the  boards,  fitting  around  cheeks  of  dormers 


CARPENTRY. 


337 


and  forming  saddles  behind  chimneys.  This  waste  is  not 
readily  calculated  and  must  be  determined  by  the  actual 
conditions  as  well  as  by  the  care  exercised  by  the  men  in 
utilizing  the  cuttings.  In  covering  large  areas  a  great  deal 
of  material  can  be  saved  by  ordering  the  lengths  of  boards  to 
suit  the  spacing  of  the  rafters. 

Flooring.— In  estimating  matched  flooring,  a  square  foot  of 

stuff  is  considered  to  be  1  ft.  B.  M.  If  the  flooring  is  3  in. 
or  more  in  width,  add  one-quarter  to  the  actual  number  of 
board  feet,  to  allow  for  waste  of  material  in  forming  the 
tongue  and  groove ;  if  less  than  3  in.  wide,  add  one-third. 
Flooring  of  in.,  finished  thickness,  is  considered  to  be  li 
in.  thick ;  and  for  calculating  it  the  following  rule  may  be 
used  :  Increase  the  surface  measure  50  per  cent.  (This  consists 
of  25  per  cent,  for  extra  thickness  over  1  in.,  and  25  per  cent, 
for  waste  in  tonguing  and  grooving.)  To  this  amount  add  5 
per  cent,  for  waste  in  handling  and  fitting. 

In  figuring  the  area  of  floors,  the  openings  for  stairs,  fire¬ 
places,  etc.  should  be  deducted. 

Siding.— Siding  is  usually  measure^  oj  the  superficial  foot. 
No  deduction  should  be  made  for  ordinary  window  or  door 
openings,  as  these  usually  balance  the  waste  in  cutting  and 
fitting.  Careful  attention  must  be  given  to  the  allowance  for 
lap.  If  6"  (nominal  width,  actual  width  5|  in.)  siding,  laid 
with  1"  lap,  is  used,  add  one-quarter  to  the  actual  area,  in 
order  to  obtain  the  number  of  square  feet  of  siding  required. 
If  4"  stuff  is  used,  add  one-third  to  the  actual  area.  When,  as 
above  noted,  no  alloAvance  is  made  for  openings,  the  corner 
and  baseboards  need  not  be  figured  separately. 

Cornices. — Cornices  may  be  measured  by  the  running  foot, 
the  molded  and  plain  members  being  taken  separately.  A 
good  method  of  figuring  cornices  is  as  follows :  Measure  the 
girth,  or  outline,  and  allow  1  cent  for  each  inch  of  girth,  per 
lineal  foot.  This  price  will  pay  for  material  and  for  setting, 
the  cost  of  the  mill  work  being  estimated  at  50  per  cent.,  or  j 
cent. 

Quantity  of  Material  Set  per  Day. — It  is  impossible  to  esti¬ 
mate  this  exactly,  as  it  depends  on  the  skill  of  the  artisan, 
his  rapidity  of  working,  the  ease  or  difficulty  of  the  work, 


338 


ESTIMATING. 


besides  numerous  accidental  circumstances.  The  subjoined 
figures,  while  founded  on  knowledge  gained  in  many  years’ 
experience,  are  only  intended  to  give  an  idea  of  the  relative 
quantities,  and  not  as  a  standard  to  be  adhered  to  in  all  cases. 
The  estimates  are  based  on  a  9-hour  day,  and  wages  of  $2.25 
per  day.  If  the  hours  or  pay  be  less  or  greater,  the  results  will 
be  correspondingly  diminished  or  increased.  Unless  other¬ 
wise  noted,  the  figures  represent  the  labor  of  two  men 
working  together. 


Quantities  of  Material  Put  in  Place  per  Day. 


Class  of  Material. 

Feet  B.  M. 
or  Number. 

Remarks. 

Studding,  2"  X  4"  or  2"  X  6" 

600-800 

Wall  or  Partition.- 

Rafters . 

Floor  joists,  2"  X  10"  or 

500-600 

3"  X  12" . 

1,500 

Sheathing,  unmatched . 

1,000 

Laid  horizontally. 

Sheathing,  unmatched . 

800 

Laid  diagonally. 

Sheathing,  matched  . 

800 

Laid  horizontally. 

Sheathing,  matched . 

600 

Laid  diagonally. 

Sheathing,  roof . 

1,000 

Plain  gable  roof. 
Much  cut  up  by 

Sheathing,  roof. . 

500 

hips,  valleys,  dor¬ 
mers,  etc. 
Includes  fitting 
and  setting  cor- 

Siding  . 

700 

ner  boards,  base, 
trim,  and  scaf¬ 
folding. 

Posts  and  beams  over  cel- 

400-500 

Includes  scarfing 

lars  . 

and  doweling. 
For  base  and 

Plaster  grounds,  lineal  feet, 

400 

wainscot,  leveled 

per  man . 

and  straightened 
in  good  shape. 

Bridging,  number  of  pairs, 

12 

Includes  cutting 

per  hour,  per  man . 

and  setting. 

False  jambs  around  open¬ 
ings,  per  hour,  per  man 

1 

Nails.— To  calculate  the  quantity  of  nails  required  in 
executing  any  portion  of  the  work,  the  following  table,  based 
on  the  use  of  cut  nails,  will  be  found  useful : 


i 


CARPENTRY. 


33^ 


Table  for  Estimating  Quantity  of  Nails. 


Material. 

Pounds 

Required. 

Name  of  Nail. 

1,000  shingles . 

5 

4d. 

1,000  laths  . 

7 

3d. 

1,000  sq.  ft.  of  beveled  siding... 

18 

6d. 

1,000  sq.  ft.  of  sheathing . 

20 

8d. 

1,000  sq.  ft.  of  sheathing . 

25 

lOd. 

1,000  sq.  ft.  of  flooring  . 

30 

8d. 

1,000  sq.  ft.  of  flooring . 

40 

lOd. 

1,000  sq.  ft.  of  studding  . . 

15 

lOd. 

1,000  sq.  ft.  of  studding  . 

5 

20d. 

1,000  sq.  ft.  of  furring  1"  X  2" 

10 

lOd. 

1,000  sq.  ft.  £"  finished  flooring 

20 

8d.  to  lOd.  finish 

1,000  sq.  ft.  1±"  finished  flooring 

30 

lOd.  finish 

ESTIMATING  COSTS 

The  character  of  the  work,  which  must  be  determined  by 
the  spirit  and  letter  of  the  specifications,  will  be  the  control¬ 
ling  factor  in  fixing  costs.  In  the  case  of  material,  where 
the  requirements  are  exacting  and  demand  a  grade  of  material 
which  can  only  be  obtained  by  special  selection,  an  extra 
rate  must  always  be  considered.  This  is  best  secured  by  con¬ 
tracting  with  the  lumber  merchants  for  the  supply  of  the 
material  to  strictly  accord  with  the  architect’s  stipulation. 
The  matter  of  labor,  however,  is  One  on  which  too  much  care 
and  forethought  cannot  be  expended.  \\  hat  may  be  con¬ 
sidered  satisfactory  work  by  one  contractor  would  be  con¬ 
sidered  inferior  by  another,  and  this  often  accounts  lor  the 
great  differences  in  estimates. 

Cost  per  Square  Foot. — For  all  classes  oi  materials  that 
enter  into  the  general  framing  and  covering  oi  a  building,  a 
close  estimate  may  be  made  by  analyzing  the  cost  per  square 
foot  of  surface ;  that  is,  the  cost  of  labor  and  materials— studs 
and  sheathing  in  Avails,  joists  and  flooring  in  floors,  etc.— 
required  for  a  definite  area  should  be  closely  determined, 
and  this  cost,  divided  by  the  area  considered,  will  give  the 
price  per  square  foot.  If  the  corresponding  whole  area  is 
multiplied  by  the  figure  thus  obtained,  the  result  will,  of 
course,  be  the  cost  of  that  portion  of  the  Avork,  M  bile  it  is 


340 


ESTIMATING. 


usual  to  adopt  a  uniform  rate  for  the  various  grades  of  work, 
a  careful  analysis  will  show  that  roof  sheathing  in  place 
costs  more  than  wall  sheathing,  owing  to  its  position ;  and 
that  the  studs  in  walls  and  partitions  cost  more  than  floor 
joists,  as  they  are  lighter  and  require  more  handling. 

The  following  example  shows  how  to  determine  the  cost 
per  square  foot  of  flooring,  and  indicates  the  general  method 
to  he  pursued  in  like  cases.  The  area  used  in  calculation  is  a 
square  of  100  sq.  ft.  The  cost  of  labor  is  estimated  at  50  per 
cent,  of  that  of  the  materials,  which  experience  has  shown 
to  be  a  very  close  approximation  to  the  actual  cost  of  general 
carpenter  work. 

Cost  of  Finished  Floor  per  Square. 

Joists,  hemlock,  8  pieces,  3  in.  X  10  in.  X  10  ft.  =  200  ft. 

B.  M.  at  $14.00  per  M . $  2.80 

Bridging,  hemlock,  7  sets,  2  in.  X  3  in.  X 1.  ft.  4  in.  =  9  ft. 

B.  M.  at  $14.00  per  M . 13 

Rough  flooring,  hemlock,  £  in.  thick,  laid  diagonally, 

100  ft.  +  25  ft.  +  10  ft.  =  135  ft.  B.  M.  at  $17.00  per  M  2.29 
Finished  flooring,  white  pine,  £  in.  thick,  125  ft.  B.  M.  at 

$22.00  per  M .  2.75 

Nails,  about  3  lb.  at  $1.80  per  100  lb . 05 

Labor,  50  per  cent,  of  cost  of  materials .  3.99 

Total  cost  for  100  sq.  ft . $12.01 

Cost  per  square  foot,  $12.01  -p  100  =  12  cents. 

A  similar  method  may  be  followed  in  estimating  the  cost 
of  interior  finish,  paneling,  doors,  etc. 

Cost  per  Thousand  Feet. — The  following  analysis  shows  the 


general  method  of  estimating  rough  carpenter  work : 

Cost  of  1,000  Ft.  B.  M.  of  Hemlock. 

Including  Framing. 

1,000  ft.  of  hemlock . $14.00 

Nails  and  spikes,  allowing  100  lb.  to  3,000  ft.  of  lumber, 

at  $1.80  per  100  lb . 60 

Labor,  taking  50  per  cent,  of  the  cost  of  material  as  cost 

of  framing .  7.00 

Cost  per  thousand  feet  B.  M 


$21.60 


JOINERY. 


341 


Cost  of  Miscellaneous  Items  of  Carpentry. 


Class  of  Work. 

Cost. 

Remarks. 

Setting  window  frames  in 

$  .30 

Each ;  about  1  hour  re- 

wooden  buildings . 

Furring  brick  walls  1"X 

quired. 

.02* 

Per  sq.ft. ;  includes  labor, 

2"  strips,  12"  centers . 

material,  and  nails. 

Furring  brick  walls,  1"  X 

Oil 

Per  sq.  ft. 

2"  strips,  16"  centers..... 

Cutting  holes  and  fitting 
plugs  in  brick  walls,  12" 

.02 

Per  sq.  ft. 

centers  . 

Cutting  holes  and  fitting 
plugs  in  brick  walls,  16" 

centers  . . 

Setting  window  frames  in 
brickwork . 

.01* 

Per  sq.  ft. 

.50 

Each  ;  includes  nails  and 
bracing. 

Door  frames  in  brickwork 

.50 

Each. 

Window  frames  in  stone- 

1.25 

Each  ;  for  ordinary  work, 

wTork  . 

screeded  and  bedded. 

Window  frames  in  stone- 

2.00 

Each ;  for  careful  work. 

work  . 

Door  frames  in  stonework 

2.00 

Each ;  for  very  careful 
work. 

Furnishing  and  setting 

1.25 

Each. 

trimmer-arch  centers... 
Arch  centers,  3i-ft.  span, 
8"  reveal . 

1.00 

Each ;  includes  supports 
and  wedges. 

JOINERY. 

Joinery  includes  all  the  interior  and  exterior  finish  put  in 
place  after  the  framing  and  the  covering  are  completed ;  as, 
for  example,  door  and  window  frames,  doors,  baseboard, 
paneling,  wainscoting,  stairs,  etc.  Most  of  these  materials 
are  worked  at  the  mill  and  brought  to  the  building  ready  to 
set  in  place. 

Frames.— In  taking  off  door  and  window  frames,  describe 
and  state  sizes.  Measure  architraves  by  the  running  foot, 
giving  width  and  thickness,  whether  molded  or  plain,  and 
state  the  number  of  plinth  and  corner  blocks. 

Sash.— State  dimensions  (giving  the  width  first);  thickness 
of  the  material,  molded  or  plain ;  stylo"  of  check-rail  and  sill 


342 


ESTIMATING. 


finish ;  thickness  of  sash  bar,  whether  plain,  single,  or  double 
hung;  and  sizes  (giving  dimensions  in  inches)  and  number 
of  lights.  Use  standard  sizes  as  much  as  possible. 

Doors.— Describe  and  state  the  sizes  and  thickness, whether 
the  framing  is  stuck-molded,  raised-molded,  or  plain ;  and 
number  of  panels,  whether  plain  or  raised.  Use  stock  sizes 
wherever  possible  and  suitable. 

Blinds. — Describe  size  and  thickness,  whether  paneled  or 
slatted  (fixed  or  movable),  and  wrhether  molded  or  plain. 

Baseboard  and  Beam  Casings. — Measure  by  the  running  foot, 
stating  width  and  thickness  of  stuff1,  and  whether  molded  or 
plain. 

Wainscoting. — Measure  by  the  superficial  foot.  State  land 
of  finish,  whether  paneled  or  plain,  and  style  of  molding  and 
panels.  Measure  wainscoting  cap  and  base  by  the  running 
foot. 

Stairways.— They  are  generally  taken  by  the  contractor  at 
so  much  per  step,  including  everything  complete  according 
to  the  specifications.  In  measuring  stairways,  take  off  the 
amount  of  rough  material  in  carriage  timbers,  and  the  planed 
lumber  in  treads,  risers,  and  strings.  Measure  balustrades  by 
the  lineal  foot.  Give  the  size  of  newels  and  the  style  of  treat¬ 
ment.  Measure  spandrel  and  stairway  paneling  the  same  as 
wainscoting. 

Fixtures. — Kitchen  dressers  may  be  taken  at  a  fixed  price 
complete,  or  at  a  fixed  rate  per  square  foot,  or  as  dressed 
lumber — drawers  and  doors  being  taken  separately.  Ward¬ 
robes,  bookcases,  mantels,  and  china  closets  should  be  treated 
separately,  and  a  fixed  price  stated.  Porches,  exterior  balus¬ 
trades,  balconies,  porte-cocheres,  etc.,  may  be  taken  at  a  price 
per  lineal  foot,  or  the  actual  quantity  of  material  may  be 
measured. 


DATA  AND  EXAM  PLESOF  ESTIMATING  JOINERYWORK. 

For  any  molded  work  which  goes  through  the  mill,  the 
usual  charge  is  1  cent  per  square  inch  of  section  per  lineal  foot 
of  the  stuff1  from  which  the  molding  is  made,  as  a  base,  from 
which  is  deducted  a  percentage,  usually  40  to  60  per  cent., 
depending  on  the  grade  of  the  material,  For  example,  a 


JOINERY. 


343 


(undressed  thickness,  1  in.)  door  casing,  5  in.  wide,  will  cost 
1  cent  X  5,  less,  say  50  per  cent.,  or  2£  cents  per  lineal  foot. 

Baseboard. — The  cost  of  material  and  fitting  in  place  may 
he  estimated  at  1  cent  per  square  inch  of  section  per  lineal  foot. 
This  is  for  pine  ;  if  hardwood  is  used,  double  this  price. 

The  same  rule  applies  also  to  chair  rails,  cap  rails,  and 
natural-finish  picture  molds. 

Paneling. — This  may  be  estimated  at  12  cents  per  square 
foot  for  1-inch  pine  stuff;  if  overt  in.,  add  simply  for  extra 
material.  If  the  paneling  is  of  hardwood  and  veneered,  add 
50  per  cent,  to  price  of  pine. 

Wainscoting. — If  plain,  this  may  be  estimated  at  cents  per 

square  foot,  the  cap  being  figured  separately  by  the  lineal  foot. 

Door  Frames. — The  following  estimate  represents  the 
approximate  cost  of  an  ordinary  door  frame.  This  and  suc¬ 
ceeding  estimates  are  given  more  to  show  how  to  make 
systematic  and  accurate  estimates  than  to  give  any  fixed 
prices. 

Cost  op  Door  Frame  in  Place. 

Size,  2  ft.  S  in.  X  6  ft.  S  in. 

Jambs  (rabbeted  for  doors),  13  ft.  G  in.;  head  jamb,  3  ft.; 
total  jambs,  16i  ft.  of  1}"  (1|")  X  6"  clear  face  material, 

at  1  cent  per  sq.  in.  per  ft.,  less  50  per  cent . $0.62 

Casing,  34£  ft.  of  Y'  (1")  X  5",  with  ground  edge  mold, 

at  same  rate . 8625 

Back-band  molding,  34|  ft.  of  (1")  X  2"  at  same  rate 

as  casing . 845 

Plinth  blocks,  4  pieces,  9"  X  If"  (2")  X  5 i"  at  1  cent  per 

sq.  in.  per  ft.,  less  50  per  cent . . . 1575 

Dadoing  and  hand-smoothing  casing,  back  band,  and 

plinth  blocks  . 50 

Nails . 05 

Putting  together  and  settingup  (2* hours) . 65 

Cost  in  place . $3.18 

D00rSi_The  subjoined  estimate  gives  the  cost  of  a  door  of 
moderate  price.  If  the  door  is  veneered  with  hardwood,  the 
cost  is  about  50  per  cent,  additional.  A  curved  door  in  a 
curved  wall  costs  about  twice  as  much  as  straight  work. 


344 


ES  TIMA  TING. 


Cost  of  Door  in  Place. 

Size,  2  ft.  8  in.  X  6  ft.  8  in. 

1|  in.  thick,  5-panel,  double  face,  flat-paneled,  and 

stuck-  or  solid-molded  door,  delivered .  $2.00 

Fitting  hinges  and  lock,  hanging  and  trimming . .  .50 

Butts,  1  pair  4"  X  4"  lacquered  steel . 40 

Mortise  lock,  brass  face  and  strike,  wood  knob,  bronze 
escutcheons . . . . 80 

Cost  in  place . „ .  $3.70 


A  fair  workman  can  hang,  trim,  and  put  hardware  on, 
including  mortise  locks,  about  6  ordinary  doors  per  day.  For 
veneered  doors,  or  those  requiring  extra  care,  not  more  than 
3  can  be  put  in  place. 

Window  Frames.— The  following  estimate  gives  approxi¬ 
mately  the  cost  of  a  window  frame  of  the  size  mentioned  : 

Cost  of  Window  Frame  in  Place. 

Size,  2  Lights,  28  in.  X  in. 

Jambs  12  ft.,  head  jamb  3£  ft.,  total  15£  ft.;  15?  ft.  X 1? in. 

(1|)  X  5  in.,  at  1  cent  per  sq.  in.  per  ft.,  less  50  per 


cent.  . $0.48 

Sill,  3£  ft.  X  1?  in.  X  5£  in.,  same  rate . _.. .  .13 

Subsill,  4  ft.  X  1£  in.  X  4  in.,  same  rate . . 16 

Blind  stop,  15i  ft.  X  ¥  in.  X  2  in . 15 

Parting  strip,  14£  ft.  X  i  in.  X  1  in . 04 

Outside  casing,  11£  ft.  x  1£  in.  X  5  in . 36 

Head  jambs,  4  ft.  X  1£  in.  X  7  in . 17 

Cap,  4  ft.  X  1£  in.  X  3  in . 08 

Molding,  4£  ft.  of  1£"  . 03 

Sill  nosing,  4  ft.  X  1£  in.  X  4  in . 10 

Apron,  4  ft.  X  v  in.  X  5  in . 10 

Cove  molding,  4  ft.  of  . 02 

Casing,  16£  ft.  X  I  in.  X  5  in . .  .41 

Back  band,  16£  ft.  X  1?  in.  X  1£  in . 12 

Sash  stop,  14jj  ft.  X  i  in.  X  H  in . 05 

Labor  for  frame  complete,  with  outside  casing  attached 
at  mill,  and  for  setting  inside  casing  at  building .  1.00 


Total  cost . $3.40 


JOINER  Y. 


345 


Windows. — The  cost  of  an  ordinary  window  may  be  esti¬ 
mated  as  follows : 


Cost  of  Sash  in  Place. 

Size ,  2  Lights ,  28  in.  X  28  in. 

Cost  of  2  sashes  If  in.  thick,  at  mill . $1.15 

Glass,  first-quality  double-thick  American,  and  setting  1.75 

Sash  weights,  35  lb.,  at  1  cent  per  lb . 35 

Cord  for  weights,  22£  ft.,  at  £  cent  per  ft . 11 

Sash  lifts,  2 . 05 

Sash  lock  . - . . 25 

Hanging  sash  and  putting  on  stops . 50 


Cost  in  place . $4.16 


For  curved  sash  in  curved  walls,  the  cost  is  about  twice 
that  of  straight  work. 

Stairs.— -The  cost  per  step  for  an  ordinary  stairway,  con¬ 
structed  according  to  the  following  specifications,  is  about 
$3.00.  For  a  better  class  of  work,  add  about  one-quarter  to 
this  price. 

Length  of  step,  3  ft. ;  tread,  Georgia  pine ;  riser,  white 
pine;  open  stringer,  white  pine;  nosing  and  cove;  dovetail 
balusters,  square  or  turned;  rail  2.’  in.  X  3  in.;  6"  start  newel, 
cherry;  two  4"  square  angle  newels,  with  trimmed  caps  and 
pendants;  simple  easements;  furred  underneath  for  plaster¬ 
ing;  treads  and  risers  tongued  together,  housed  into  wall 
stringers,  wedged,  glued,  and  blocked. 

The  material  of  such  a  stairway  will  cost  about  $1.84  per 
step.  This  rate  includes  landing  facia  and  balustrade  to 
finish  on  upper  floor.  The  labor  on  the  same,  millwork,  and 
setting  in  place,  is  about  $1.16  per  step.  For  example,  fora 
stairs  having  17  steps  and  landing  balustrade  (including 
return,  about  14  ft.),  the  entire  cost  will  be  17  X  $3.00  =  $51.00, 
of  which  $31.28  will  represent  cost  of  dressed  lumber,  inclu¬ 
ding  turned  balusters  and  newels  and  worked  rail,  and  $10.72 
will  represent  cost  of  labor  in  housing  stringers,  cutting, 
mitering,  and  dovetailing  steps,  working  easements,  fitting 
and  bolting  rails,  and  erecting  stairway  in  building. 


346 


ESTIMATING. 


Verandas. — For  small  dwellings,  it  has  been  found  by  experi¬ 
ence  that  a  veranda  built  on  the  following  specifications  will 
cost  about  §2.25  per  lineal  foot : 

Width,  5  ft.;  posts,  turned,  set  6  to  8  ft.  on  centers;  floor 
timbers,  2  in.  X  6  in.;  flooring,  white  pine,  sound  grade; 
rafters,  2  in.  X  4  in.  dressed  ;  purlins,  2  in.  X  4  in.,  set  2  ft.  on 
centers :  rqof  sheathing,  matched  white  pine ;  box  frieze  and 
angle  mold ;  angle  and  face  brackets ;  steps ;  no  balustrade. 

To  include  balustrade,  with  2"  turned  balusters,  add  about 
fiO  cents  per  lineal  foot. 

For  a  veranda,  built  according  to  the  following  specifica 
tions,  the  cost  will  be  §4.00  per  lineal  foot : 

Width,  8  ft. ;  columns,  9"  turned ;  box  pedestals ;  box 
cornice  and  gutter;  level  ceiling;  roof  timbers,  2  in.  X  6  in.; 
roof  covered  with  matched  boards ;  a  good  grade  of  tin ; 
floor  timbers,  2  in.  X  8  in.;  floor,  l\r'  white  pine,  second  grade, 
with  white-lead  joints ;  no  balustrade. 

Including  balustrade,  with  2\"  turned  balusters,  rail  and 
base  to  suit,  add  80  cents  per  lineal  foot. 

Where  a  portion  of  the  veranda  is  segmental  or  semi¬ 
circular,  a  close  approximation  to  the  cost  will  result  if  the 
girth  of  the  circular  part  is  measured,  and  a  rate  fixed  at 
twice  that  for  straight  wrork  of  the  same  length.  This  applies 
to  veranda  framing,  roofing,  casing,  and  balustrades. 


ROOFING. 

/ 


ROOF  MENSURATION. 

While  the  ordinary  principles  of  mensuration  are  all  that 
are  necessary  to  calculate  any  roof  area,  yet  the  modern 
house,  with  its  numerous  gables  and  irregular  surfaces,  intro¬ 
duces  complications  which  render  some  further  explanation 
of  roof  measurement  desirable.  The  most  common  error 
made  in  figuring  roofs,  and  one  which  should  be  carefully 
guarded  against,  ist  that  of  using  the  apparent  length  of  slopes, 
as  shown  by  the  plan  or  side  elevation,  instead  of  the  true 
length,  obtaiued  from  the  end  elevations. 


ROOFING. 


347 


The  area  of  a  plain  gable  roof,  as  shown  in  end  and  side 
elevations  in  (a),  Fig.  1,  is  found  by  multiplying  the  length  gj 
by  the  slope  length  b  d,  and  further  multiplying  by  2,  for  both 
sides.  The  area  of  the  gable  is  found  by  multiplying  the 
width  of  the  gable  a  d  by  the  altitude  c  b  and  dividing  by  2. 

At  ( b )  is  shown  the  plan  and  the  elevation  of  a  hip  roof, 
having  a  deck  z.  The  pitch  of  the  roof  being  the  same  on 
each  side,  the  line  c  d  shows  the  true  length  of  the  common 
rafter  Im,  ce  being  the  height  of  the  deck  above  ad.  At  (c)  is 
shown  the  method  of  determining  the  true  lengths  of  the 
hips,  and  the  true  size  of  one  side  of  the  roof.  Let  abed 
represent  the  same  lines  as  the  corresponding  ones  in  ( b ). 


(b) 


Fig.  1. 


From  the  line  a  d,  through  b  and  c,  draw  perpendiculars, 
as  g  h  and  e f ;  lay  off  from  g  and  e  on  these  lines  the  length  of 
the  common  rafter  a b,  in  (b),  and  draw  the  lines  ah  and 
df;  then  the  figure  ahfd  will  show  the  true  shape  and 
size  of  that  side  of  the  roof  shown  in  the  elevation  in  (b). 
The  triangle  d  ef  equals  in  area  the  triangle  ag  h  or  a  similar 
triangle  a  i  h.  Hence,  the  portion  of  the  roof  a  hfd  is  equal 
in  area  to  the  rectangle  aife ,  whose  length  is  one-half  the 
sum  of  the  eaves  and  deck  lengths,  and  whose  breadth  is  the 
length  of  a  common  rafter. 

A  method  of  obtaining  the  lengths  of  valley— applicable 
also  to  hip  rafters— is  shown  at  (d),  which  is  the  plan  of  a 


348 


ESTIMATING. 


hip-and-gable  roof.  To  ascertain  the  length  of  the  valley 
rafter  a  b,  draw  the  line  a  c  perpendicular  to  a  b  and  equal  in 
length  to  the  altitude  of  the  gable ;  then  draw  the  line  c  b, 
which  will  be  the  length  required. 

As  an  example  of  roof  mensuration,  the  number  of  square 
feet  of  surface  on  the  roof  shown  in  Fig.  2  will  be  calculated. 
The  area  of  the  triangular  portion  acb  is  equal  to  one-half 
the  base  a  b,  multiplied  by  the  slope  length  of  c  d.  The  latter 
"is  found  by  making  c  c',  perpendicular  to  d  c,  equal  to  the 


height  of  the  ridge  (10  ft.)  above  a  b,  and  drawing  c' d,  which 
is  the  required  slope  length.  Using  dimensions,  the  area  of 

acb  is - - — —  =  158.1  sq.  ft. 

A 

The  area  of  the  trapezoid  gfili  is  one-half  the  sum  of  fi 
and  g  h,  multiplied  by  the  true  length  of  h  i,  which,  by  laying 
offii',8  ft.  along / i,  and  drawing  V  h ,  is  found  to  be  10  ft.  7|  in., 

or,  say,  10.6  ft.  Then  gfi  h  —  1  X  10.6  =  100.7  sq.  ft.;  or, 


ROOFING. 


349 


for  the  two  slopes  of  the  gable,  the  area  is  201.4  sq.  ft.  As  the 
opposite  gable  is  the  same  size,  the  area  of  the  two  is 

201.4  X  2  =  402.8  sq.  ft. 

The  area  of  q  p  n  k  is  equal  to  the  area  qpw,  minus  the 
area  k  n  w,  which  is  covered  by  the  intersecting  gable  roof. 
The  area  qpw  is  equal  to  the  area  acb,  or  158.1  sq.  ft.  The 
area  of  knw  is  equal  to  4  the  product  of  nw  and  the  slope  of 
sk  (which,  by  laying  off  kk'  equal  to  the  height  of  the  gable, 
5.5  ft.,  and  drawing  sk',  is  found  to  be  nearly  7.5  ft.).  Then 

area  &  raw  =  — £ — —  =  48.7  sq.  ft.,  which,  deducted  from- 

158.1  sq.  ft.,  shows  the  area  of  qp  n  k  to  be  109.4  sq.  ft. 

The  area  of  ap  q  c  is  multiplied  by  the  true  slope 

length  of  tv,  which  is  tv',  measuring  15.25  ft.  Substituting 

dimensions,  the  area  is  found  to  be  ^  X  15.25  =  228.7  sq.  ft. 

From  this  deduct  the  area  of  yzu,  which  is  the  portion 
covered  by  the  intersecting  gable  roof.  The  true  length 
of  t  u  along  the  slope  is  t  u' ,  which  measures  12  ft.;  hence,  the 

area  of  yzu  is  14  *■  12  U  84  sq.  ft.  The  net  area  of  ap  q  c  is, 
z 

therefore,  228.7  —  84  =  144.7  sq.  ft,;  bcqw  being  equal  to 
apqc,  its  area  is  the  same,  making  the  area  of  both  sides 

289.4  sq.  ft. 

The  area  of  kn ml  is  '’HZLZ  x  ml',  the  slope  length  of 

m  l.  Substituting  dimensions,  the  area  is  — ^  X  8.5  —  114. 7 

sq.  ft.  As  klxw  is  equal  to  knml,  the  area  ol  both  is 

229.4  sq.  ft.  Adding  the  partial  areas  thus  obtained,  the  sum 

is  158.1  +  402.8  +  109.4  +  289.4  +  229.4  =  1,189.1  sq.  ft.,  or  11.9 
squares.  _ _ 

SHINGLES. 

Measurement.— In  measuring  shingle  roofing,  it  is  necessary 
to  know  the  exposed  length  of  a  shingle,  which  is  found  bj 
deducting  3  inches— the  usual  cover  of  the  upper  shingle 
over  the  head  of  the  third  shingle  below  it-from  the 
w 


350 


ESTIMATING. 


length ;  dividing  the  remainder  hy  3,  the  result  will  be  the 
exposed  length ;  multiplying  this  by  the  average  width  of 
a  shingle,  the  product  will  be  the  exposed  area.  Dividing 
14,400,  the  number  of  square  inches  in  a  square,  by  the 
exposed  area  of  1  shingle,  will  give  the  number  required  to 
cover  100  sq.  ft.  of  roof.  For  example,  it  is  required  to 
compute  the  number  of  shingles,  18  in.  X  4  in.,  necessary 
to  cover  100  sq.  ft.  of  roof.  With  a  shingle  of  this  length, 

the  exposure  will  be  ^  =  5  in. ;  then  the  exposed  area  of 

O 

1  shingle  is  4  in.  X  5  in.,  or  20  sq.  in.,  and  1  square  requires 
14,400  -f-  20  =  720  shingles. 

In  estimating  the  number  of  shingles  required,  an  allow¬ 
ance  should  always  be  made  for  waste. 

The  following  table  is  arranged  for  shingles  from  16  to 
27  in.  in  length,  4  and  6  in.  in  width,  and  for  various  lengths 
of  exposure. 


Table  for  Estimating  Shingles. 


Exposure 

to 

Weather. 

Inches. 

No.  of  Sq.  Ft  of  Roof 
Covered  by  1,000 
Shingles. 

No.  of  Shingles 
Required  for  100 

Sq.  Ft.  of  Roof. 

4  In.  Wide. 

6  In.  Wide. 

4  In.  Wide. 

6  In.  Wide. 

4 

Ill 

167 

900 

600 

5 

139 

208 

720 

480 

6 

167 

250 

600 

400 

7 

194 

291 

514 

343 

8 

222 

333 

450 

300 

Shingles  are  classed  as  shaved  or  breasted,  and  sawed 
shingles.  The  former  vary  from  18  to  30  in.  in  length,  and 
are  about  £  in.  thick  at  the  butt  and  in.  at  the  top ;  the 
latter  are  usually  from  14  to  18  in.  long,  and  of  various  thick¬ 
nesses,  five  18"  shingles,  placed  together,  measuring  2$  in. 
..t  the  butt,  the  thickness  of  each  at  the  top  being  ^  in. 

Strictly  first-class  shingles  are  generally  given  a  brand  of 
XXX,  and  those  of  a  slightly  poorer  quality  are  termed 


ROOFING. 


351 


No.  2 ;  but  in  some  sections  of  the  country,  the  brand  A  is 
general;  thus,  “choice  A”  or  “  standard  A”  are  practically 
equivalent  to  the  XXX  shingles. 

Shaved  shingles  are  usually  packed  in  bundles  of  500,  or  2 
bundles  per  thousand.  Sawed  shingles  are  made  up  into 
bundles  of  250,  and  are  sold  on  a  basis  of  4  in.  width  for  each 
shingle.  If  the  wider  ones  are  ordered,  the  cost  per  thousand 
is  correspondingly  increased.  For  example,  if  it  requires 
1,000  of  4"  shingles  to  cover  a  roof  area,  and  6"  ones  were 
ordered,  only  two-thirds  as  many,  or  667,  would  be  needed 
and  furnished,  while  the  cost  would  be  that  of  1,000  standard- 
width  shingles. 

Shingles  cost  from  $3.00  to  $5.00  per  thousand,  according 
to  material  and  grade.  Dimension  shingles— those  cut  to  a 
uniform  width— of  prime  cedar,  shaved,  |  in.  thick  at  the 
butt,  and  Jg  in.  at  the  top,  will  cost  $0.00  to  $10.00  per  thou¬ 
sand,  but  such  shingles  are  usually  6  in.  wide  and  24  in.  long, 
so  that  a  less  number  will  be  required  per  square  than  of 
ordinary  shingles. 

A  fairly  good  workman  will  lay  about  1,500  shingles  pel 
day  of  9  hours,  on  straight,  plain  work ;  while,  in  working 
around  hips  and  valleys,  the  average  will  be  about  1,000  pesr 

day. 

Cost.— The  method  of  estimating  the  cost  of  shingle  roofing 
is  as  follows : 

Cost  of  1,000  Shingles  in  Place. 

Exclusive  of  Sheathing. 

1,000  shingles  XXX .  $5-00 

Labor :  1  man  can  lay  1,500  shingles  per  day ;  wages  being 

$2.25,  the  cost  per  thousand  is. .  1.50 

Nails,  about . 25 

(Flashing,  about  10  cents  per  sq.  ft.)  . .  . 

Cost  per  thousand,  about .  $6.75 


SLATING. 

Measurement.— In  measuring  slating,  the  method  of  deter¬ 
mining  the  number  of  slates  required  per  square  is  similar  to 
that  given  for  shingling ;  but,  in  slating,  each  course o^  erlaps 


352 


ESTIMATING. 


only  two  of  the  courses  below,  instead  of  three,  as  in  shingling. 
The  usual  lap,  or  cover  of  the  lowest  course  of  slate  by  the 
uppermost  of  the  three  overlapping  courses,  is  3  in.;  hence, 
to  find  the  exposed  length,  deduct  the  lap  from  the  length  of 
the  slate,  and  divide  the  remainder  by  2.  The  exposed  area 
is  the  width  of  the  slate  multiplied  by  this  exposed  length, 
and  the  number  required  per  square  is  found  by  dividing 
14,400  by  the  exposed  area  of  1  slate. 

Thus,  if  14"  X  20"  slates  are  to  be  used,  the  exposed  length 
20 _ 3 

will  be  — - —  =  in.;  the  exposed  area  will  be  14X8i 

A 

—  119  sq.  in.,  and  the  number  per  square  will  be  14,400  119 

~  121  slates. 

The  following  rules  should  be  observed  in  measuring 
slating :  Eaves,  hips,  valleys,  and  cuttings  against  walls  are 
measured  extra,  1  ft.  wide  by  their  whole  length,  the  extra 
charge  being  made  for  waste  of  material  and  the  increased 
labor  required  in  cutting  and  fitting.  Openings  less  than  3 
sq.  ft.  are  not  deducted,  and  all  cuttings  around  them  are 
measured  extra.  Extra  charges  are  also  made  for  borders, 
figures,  and  any  change  of  color  of  the  work,  and  for  steeples, 
towers,  and  perpendicular  surfaces. 

The  following  table,  based  on  3"  lap,  gives  the  sizes  of  the 
American  slates,  and  the  number  of  pieces  required  per 
square. 

Number  of  Slates  per  Square. 


Size. 

Inches. 


6X12 
7X12 
8X12 
9X12 
7X14 
8X14 
9X  14 
10  X  14 
8X16 


Number 

of 

Pieces. 


533 

457 

400 

355 

374 

327 

291 

261 

277 


Size. 

Inches. 


9X  16 
10  X  16 
9X18 

10  X  18 

11  X  18 

12  X  18 
10X20 
11  X  20 
12X20 


Number 

of 

Pieces. 


246 

221 

213 

192 

174 

160 

169 

154 

141 


Size. 

Inches. 


14X20 

11  X  22 

12  X  22 

13  X  22 
14X22 
12X24 
13X24 

14  X  24 
16  X  24 


Number 

of 

Pieces. 


121 

138 

126 

116 

108 

114 

105 

98 

86 


ROOFING. 


353 


Cost.— The  cost  of  slating  may  he  estimated  as  follows : 


Cost  op  1  Square  op  Slating. 

Slates,  8  in.  X  12  in . . 85.00 

Labor :  1  slater  will  average  2  squares  per  day ;  wages 

being  82.00  per  day,  1  square  will  cost .  1.00 

Nails,  8"  X  12"  slates  require  5  lb.  9  oz.  (5.6  lb.)  of  galva¬ 
nized  nails  per  square,  which,  at  $2.20  per  100  lb.,  cost.  .12 

Roofing  felt,  1  roll . .  2.40 

Labor  and  nails  for  applying  felt . . . 15 

Flashing  will  cost  about  10  cents  per  sq.  ft .  . 

Cost  per  square  . $8-67 


This  figure  is  exclusive  of  roof  sheathing,  the  cost  of  which 
may  be  estimated  as  shown  for  hemlock  framing,  on  page  340. 

The  cost  of  slating  per  square  varies  from  7  to  13  cents  per 
sq.  ft.,  depending  on  the  class  of  work. 


TIN  ROOFS. 

In  estimating  tin  (and  also  other  metal)  roofs,  hips  and 
valleys  are  measured  extra  their  entire  length  by  1  ft.  in 
width,  to  compensate  for  increased  labor  and  waste  of  mate¬ 
rial  in  cutting  and  laying.  Gutters  and  conductor,  or  leader, 
pipes  are  measured  by  the  lineal  foot,  1  ft.  extra  being 
added  for  each  angle.  All  flashings  and  crestings  are  meas¬ 
ured  by  the  lineal  foot.  For  seams,  addition  is  made  to 
superficial  area,  depending  on  the  kind  of  seam  used, 
whether  single-lock,  standing,  or  roll-and-cap.  No  deduc¬ 
tions  are  made  for  openings  (chimneys,  skylights,  ventilators, 
or  dormer-windows),  if  less  than  50  sq.  ft.  in  area ;  if  between 
50  and  100  sq.  ft.,  one-half  the  area  is  deducted  ;  if  over  100 
sq.  ft.  the  whole  opening  is  deducted.  An  extra  charge  is 
made  for  labor  and  waste  of  material  to  flash  around  such 
openings. 

A  box  of  roofing  tin  contains  112  sheets  14  in.  X  20  in.,  and 
weighs  from  110  to  140  lb.  per  box,  according  to  whether  it  is 
IC  or  IX  plate.  The  IC  plate,  which  is  the  most  used,  weighs 
about  8  oz.  per  sq.  ft,,  and  the  IX,  aboutlOoz.  As  there  are  con¬ 
siderable  variations  in  the  weights  of  tin  made  by  different 


354 


ESTIMATING. 


manufacturers,  a  fair  average  will  be  obtained  by  estimating 
IC  tin  at  1  lb.,  and  IX  tin  at  1£  lb.,  per  sheet.  Double-size 
roofing  tin  can  be  had  20  in.  X  28  in.,  weighing,  if  IC,  225  lb. 
per  box.  This  size  is  the  most  economical,  as  by  its  use  much 
material  and  labor  are  saved,  on  account  of  the  less  number 
of  seams  and  ribs  required. 

A  14"  X  20"  sheet  will  cover  about  235  sq  in.  of  surface, 
using  standing  joints ;  or  a  box  will  cover  about  182  sq.  ft. 
With  a  flat-lock  seam,  a  sheet  will  cover  255  sq.  in.,  allowing 
|  in.  all  around  for  joints  ;  or  a  box  will  lay  198  sq.  ft.  These 
figures  make  no  allowance  for  waste. 

Two  good  workmen  can  put  on,  and  paint  outside,  from 
250  to  300  sq.  ft.  of  tin  roofing  per  day  of  8  hours.  Tin  roofing 
will  cost  from  8  to  10  cents  per  sq.  ft.,  depending  on  the 
quality  of  material  and  workmanship. 


TILE  ROOFS. 

Tile  roofs  are  constructed  of  so  many  styles  of  tile  that  no 
general  rules  of  measurement  can  be  given,  and  every  piece 
of  work  must  be  estimated  according  to  the  particular  kind 
of  tile  used  and  the  number  of  sizes  and  patterns.  Informa¬ 
tion  on  all  these  points  are  to  be  found  in  the  catalogues  of 
tile  manufacturers. 


GRAVEL  ROOFING. 

In  gravel  roofing,  the  cost  per  square  depends  on  the  num¬ 
ber  of  thicknesses  of  tarred  felt  and  the  quantity  of  pitch 
used  per  square. 

PLASTERING. 

Plastering  on  plain  surfaces,  such  as  walls  and  ceilings,  is 
always  measured  by  the  square  yard ;  but  there  are  consid¬ 
erable  variations  in  detail  in  the  methods  of  measurement  in 
different  sections  of  the  country.  The  following  rules,  how¬ 
ever,  probably  represent  the  average  practice,  and  are  equita¬ 
ble  to  both  parties  concerned : 

On  walls  and  ceilings,  measure  the  surface  actually  plas¬ 
tered,  making  no  deduction  for  grounds  or  for  openings  of 
less  extent  than  7  superficial  yards. 


PLASTERING. 


355 


Returns  of  chimney  breasts,  pilasters,  and  all  strips  of 
plastering  less  than  12  in.  in  width,  measure  as  12  in.  wide. 

In  closets,  add  one-half  to  the  actual  measurement;  if 
shelves  are  put  up  before  plastering,  charge  double  measure¬ 
ment. 

For  raking  ceilings  or  soffits  of  stairs,  add  one-half  to 
measurement ;  for  circular  or  elliptical  work,  charge  two 
prices ;  for  surfaces  of  domes  or  groined  ceilings,  charge  three 
prices. 

Round  corners  and  arrises  (other  than  chimney  breasts) 
should  be  measured  by  the  lineal  foot. 

On  interior  work,  increase  the  price  5  per  cent,  for  each  12 
ft.  above  the  ground  after  the  first.  For  outside  work,  add 
1  per  cent,  for  each  foot  above  the  lower  20  ft. 

All  repairing  and  patching  should  be  done  at  agreed 
prices. 

Stucco  Work.— Cornices  composed  of  plain  members  and 
panel  work  are  measured  by  the  square  foot.  Enriched  cor¬ 
nices,  with  carved  moldings,  are  measured  by  the  lineal  foot. 
When  moldings  are  less  than  12  in.  in  girth,  measurement  is 
taken  by  the  lineal  foot ;  when  over  12  in.,  superficial  meas¬ 
urement  is  used.  For  internal  angles  or  miters,  add  1  ft.  to 
length  of  cornice ;  and  for  external  angles,  add  2  ft.  to  length. 
Sections  of  cornices  less  than  12  in.  measure  as  12  in.  Add 
one-half  for  raking  cornices. 

For  cornices  or  moldings  abutted  against  wall  or  plain 
surface,  add  1  ft.  to  length  of  cornice ;  if  against  soffit  of 
stairs  or  other  inclined  or  coved  surface,  add  2  ft.  to  length 
of  cornice.  Octagonal,  hexagonal,  and  similar  cornices,  less 
than  10  ft.  in  single  stretches,  measure  one  and  one-half  times 
the  length. 

For  circular  or  elliptical  work,  charge  double  prices ;  for 
domes  and  groins,  charge  three  prices. 

Column  and  pilaster  capitals,  frieze  enrichments,  and  work 
of  this  character,  which  require  artistic  treatment,  are  either 
made  to  conform  to  the  models  furnished  by  the  architect,  or 
they  are  modeled  from  the  architect’s  designs  and  submitted 
to  him  for  approval.  Expense  of  modeling  is  large  ;  prices 
are  usually  obtained  from  specialists  in  this  department. 


356 


ESTIMATING. 


ESTIMATES  OF  QUANTITIES  AND  COSTS. 

Plastering. — Two  plasterers  and  one  laborer  should  average 
from  60  to  70  sq.  yd.  per  day.  The  cost  of  labor  on  3-coat 
work,  costing  about  25  cents  per  sq.  yd.,  will  be  about  12 
cents.  For  2-coat  work,  costing  about  20  cents  per  sq.  yd., 
the  cost  of  the  labor  will  be  about  8  cents.  Both  of  these 
figures  on  labor  are  exclusive  of  the  cost  of  lathing. 

The  following  analyses  of  cost  of  2-  and  3-coat  plastering 
are  carefully  made,  and  may  be  relied  on  as  bases  for  esti¬ 
mates.  Very  fine  wrork  will  cost  considerably  more. 

Cost  of  100  Sq.  Yd.  of  3-Coat  Plastering. 


1,440  laths,  1£  in.  wide,  f"  spacing,  at  $2.10  per  1,000 .  $  3.02 

10  lb.  3d.  nails,  at  $2.05  per  100  lb . 20 

Labor  :  putting  on  lath,  1  day. .  2.25 

13  bu.  of  lime,  at  $.25  per  bu . .  3.25 

1  bu.  of  hair,  8  lb.,  at  $.04  per  lb . 32 

11  loads  of  plastering  sand,  at  $1.50  per  load .  2.25 

I  bbl.  of  plaster  of  Paris,  at  $1.50  per  bbl . 50 

Labor : 

Plasterer,  ot  days,  at  $3.00  per  day .  9.75 

Helper,  2£  days,  at  $1.50  per  day .  3.75 

Cartage  .  1.00 


Total .  $26.29 

Cost  per  sq.  yd.,  $26.29  -r-  100  =  26  cents,  approximately. 

Cost  of  100  Sq.  Yd.,  2-Coat  Plastering. 

Cost  of  lath  and  putting  on,  same  as  above . $  5.47 

10  bu.  of  lime,  at  $.25  per  bu . . .  2.50 

3  bu.,  or  6  lb.,  of  hair,  at  $.04  per  lb . 24 

1  load  of  sand  .  1.50 

|  bbl.  plaster  of  Paris,  at  $1.50  per  bbl .  .50 

Labor : 

Plasterer,  2\  days,  at  $3.00  per  day .  6.75 

Helper,  2\  days,  at  $1.50  per  day .  3.37 

Cartage  .  1.00 

Total .  $21.33 

Cost  per  square  yard,  $21.33  -*-  100  =  21  cents,  approxi¬ 
mately. 


PAINTING  AND  PAPERING. 


357 


Lathing.— This  is  measured  by  the  superficial  yard,  no 
openings  under  7  superficial  yards  being  deducted. 

Plastering  laths  are  about  1£  in.  wide,  £  in.  thick,  and 
usually  4  ft.  long,  the  studding  being  generally  placed  12  or 
16  in.  on  centers,  so  that  the  ends  of  the  lath  may  be  nailed 
to  them.  The  laths  are  usually  set  from  £  to  f  in.  apart, 
requiring  about  1|  or  1£  laths,  4  ft.  long,  to  coyer  1  sq.  ft. 

For  a  good  average  grade  of  work,  a  man  will  lay,  on  an 
average,  about  15  bunches,  or  1,500  laths  per  day,  while  a 
rapid  workman  will  put  on  about  2,000  laths.  The  cost  of 
nailing  up  laths  will  be  from  18  to  25  cents  per  bunch,  or  $1.80 
to  $2.50  per  thousand,  being  about  equal  to  the  cost  of  the 
laths  and  nails. 


PAINTING  AND  PAPERING. 


PAINTING. 

Painting  is  measured  by  the  superficial  yard,  girting  every 
part  of  the  work  that  is  covered  with  paint,  and  allowing 
additions  to  the  actual  surface  to  compensate  for  the  diffi¬ 
culty  of  covering  deep  quirks  of  moldings,  for  carved  and 
enriched  surfaces,  etc.  Ordinary  door  and  window  openings 
are  usually  measured  solid,  on  account  of  the  extra  time  taken 
in  working  around  them,  “  cutting  in  ”  the  window  sash,  etc. 
Porch  and  stair  balustrades,  iron  railings,  and  work  having 
numerous  thin  strips  are  also  figured  solid,  for  a  like  reason. 
Allowance  is  frequently  made  for  distance  from  ground  that 
the  work  is  to  be  done,  as  in  cornices,  balconies,  dormers,  etc., 
and  also  for  the  difficulty  of  access. 

Charges  are  usually  made  for  each  coat  of  paint  put  on,  at 
a  certain  price  per  superficial  yard  and  per  coat. 

Graining  and  marbling  (imitations  of  wood  and  stone)  and 
varnishing  are  rated  at  different  prices  from  plain  work. 

Capitals  and  columns  and  other  ornamental  work,  which 
are  difficult  to  measure,  should  be  enumerated,  and  a  clear 
description  of  the  amount  of  work  on  them  should  be  given. 

Quantities.— One  pound  of  paint  covers  from  3^  to  4  sq.  yd. 
of  wood  first  coat,  and  from  4£  to  6  sq.  yd.  for  each  addi- 


358 


ESTIMATING. 


tional  coat ;  on  brickwork,  it  will  cover  about  3  and  4  sq.  yd., 
respectively.  Colored  paint  will  cover  about  one-third  more 
surface  than  white  paint. 

Using  prepared  or  ready-mixed  paint,  1  gal.  will  cover  from 
250  to  300  sq.  ft.  of  wood  surface,  two  coats ;  for  covering 
metallic  surfaces,  1  gal.  will  be  sufficient  for  from  300  to  350 
sq.  ft.,  two  coats.  The  weight  per  gallon  of  mixed  paints 
varies  considerably,  but,  on  an  average,  may  be  taken  at 
about 1G  lb. 

Prepared  shingle  stains  will  cover  about  200  sq.  ft.  of  sur¬ 
face,  per  gallon,  if  applied  with  a  brush ;  or  this  quantity 
will  be  sufficient  for  dipping  about  500  shingles.  Rough- 
sawed  shingles  will  require  about  50  per  cent,  more  stain  than 
smooth  ones. 

One  pound  of  cold-mater  paint  will  cover  from  50  to  75  sq.  ft. 
for  first  coat,  on  wood,  according  to  surface  condition,  and 
about  40  sq.  ft.  of  brick  and  stone. 

One  gallon  of  liquid  pigment  filler,  hard  oil  finish  or  var¬ 
nish,  will  generally  cover  from  350  to  450  sq.  ft.  of  surface  for 
first  coat,  according  to  the  nature  of  wood  and  finish,  and 
from  450  to  550  sq.  ft.  for  the  second  and  subsequent  coats. 
Ten  pounds  of  paste  wood  filler  will  cover  about  400  sq.  ft. 

One  gallon  of  varnish  weighs  from  8  to  9  lb.;  turpentine, 
about  7  lb.;  and  boiled  or  raw  linseed  oil,  about  7f  lb. 

For  puttying,  about  5  lb.  will  be  sufficient  for  100  sq.  yd. 
of  interior  and  exterior  work. 

For  sizing,  about  £  lb.  of  glue  is  used  to  1  gal.  of  water. 

For  mixing  paints,  the  following  figures  represent  the  aver¬ 
age  proportions  of  materials  required  per  100  lb.  of  lead  : 


Quantities  of  Materials. 


Coat. 

Lead. 

Lb. 

Raw  Oil. 
Gal. 

Japan  Drier. 
Gal. 

Priming  coat  . 

100 

7 

1 

Second  coat . 

100 

6 

Third  coat . . 

100 

6s-7 

The  drier  is  omitted  in  the  second  and  succeeding  coats, 


PAINTING  AND  PAPERING. 


359 


unless  the  work  is  to  be  dried  very  rapidly,  as  it  is  considered 
injurious  to  the  durability  of  the  paint. 

On  outside  work,  boiled  oil  is  generally  used  in  about  the 
proportion  of  3  gal.  of  boiled  oil  to  2  gal.  of  raw  oil. 

Cost. — The  cost  of  applying  paint,  on  general  interior  and 
exterior  work,  will  average  about  twice  the  cost  of  the 
materials ;  while  for  very  plain  work,  done  in  one  color,  the 
cost  may  be  taken  at  about  H  times  that  of  the  materials. 
For  stippling,  the  cost  will  be  about  the  same  as  for  two  coats 
of  paint.  For  varnishing,  the  cost  of  labor  will  be  about  H 
times  the  price  of  the  varnish.  The  class  of  work  demanded, 
however,  will  regulate  the  actual  cost,  as  the  rubbing  down 
of  the  successive  coats  requires  the  expenditure  of  much  time. 

The  following  figures  represent  fair  average  prices,  for 
various  classes  of  work,  and  have  been  adopted  by  the 
Builders’  Exchange  of  a  large  Eastern  City : 


Interior  Work.  Cost  per 

Square  Yard. 

1  coat  paint,  1  color . - . $0.12 

1  coat  paint,  2  colors  . 15 

2  coats  paint,  2  colors . 20 

3  coats  paint,  2  colors . 25 

2  coats  paint,  3  colors . 25 

3  coats  paint,  3  colors . 32 

1  coat  shellac . 10 

Walls,  1  coat  size,  2  coats  paint . 20 

Walls,  1  coat  size,  3  coats  paint,  stipple . 30 

Hardwood  Finish. 

1  coat  paste  filler,  1  coat  varnish . $0.30 

1  coat  paste  filler,  2  coats  varnish . 40 

1  coat  paste  filler,  3  coats  varnish . 50 

Natural  Finish. 

1  coat  liquid  filler,  1  coat  varnish .  $0.20 

1  coat  liquid  filler,  2  coats  varnish  . 25 

1  coat  liquid  filler,  3  coats  varnish,  rubbed . 40 


Floors :  filling,  shellacing,  varnishing,  or  waxing,  2  coats  .35 


360 


ESTIMATING. 


Tinting  Walls. 

Distemper  Color.  Cost  per 

Square  Yard. 

Tinting,  50  yards,  or  less  . .  $0.09 

Tinting,  50  yards,  or  more . . . 07 

Patching  and  washing  walls  . 07 


Exterior  Painting. 
Woodwork. 

1  coat,  new  work . 

2  coats,  new  work,  2  colors . 

2  coats,  new  work,  3  colors . . . 

3  coats,  new  work,  2  colors . 

3  coats,  new  work,  3  colors . . 

Brickwork. 


1  coat .  $0.12 

2  coats  . 18 

3  coats  . 25 

Sanding. 

2  coats  paint,  1  coat  sand . .'. .  $0.28 

3  coats  paint,  1  coat  sand . 35 

3  coats  paint,  2  coats  sand  . 50 


Miscellaneous. 

Dipping  shingles,  per  1,000  . 

Additional  coat,  per  1,000 . 

Blinds,  per  foot,  1  coat  . 

Fence,  per  foot,  1  coat  4  feet  high,  wood 

Iron  fence,  per  foot,  1  coat . 

Tin  roof,  per  yard,  1  coat . 


PAPERING. 

Papering  is  usually  figured  per  roll,  put  on  the  wall.  The 
paper  is  generally  18  in.  wide,  and  is  in  either  8-yd.  or  16-yd. 
tolls.  On  account  of  waste  in  matching,  etc.,  it  is  difficult  to 
estimate  very  closely  the  number  of  rolls  required,  but  an 
approximate  result  may  be  obtained  as  follows :  Divide  the 
perimeter  of  the  room  by  1£  (the  width  of  paper  in  feet) ;  the 


$3.00 

.50 

.08 

.12 

.08 

.05 


$0.10 

.18 

.20 

.25 

.28 


MISCELLANEOUS  NOTES. 


361 


result  will  be  the  number  of  strips.  Find  the  number  of 
strips  that  can  be  cut  from  a  roll,  and  divide  the  first  result 
by  the  second ;  the  quotient  will  be  the  number  of  rolls 
required.  No  openings  less  than  20  sq.  ft.  in  area  should  be 
deducted,  in  order  to  compensate  for  cutting  and  fitting  at 
such  places.  Add  about  15  per  cent,  to  the  area  to  allow  for 
waste.  The  border,  whether  wide  or  narrow,  is  usually 
figured  as  1  roll  of  paper. 

The  cost  of  paper  is  extremely  variable,  ranging  from  15 
cents  to  $6.00  per  double  roll ;  the  average  cost  is  probably 
20  to  25  cents  per  roll  for  ordinary  houses.  Paper  hanging 
costs  from  30  to  75  cents  per  double  roll,  with  strips  butted, 
the  former  figure  being  for  the  usual  grade  of  work ;  with 
lapped  strips,  the  cost  is  less,  being  from  20  to  25  cents  per 
roll.  Sometimes  an  extra  charge  is  made  for  papering 
ceilings. 

MISCELLANEOUS  NOTES. 

Plumbing.— An  approximate  figure  for  cost  of  plumbing  is 
10  per  cent,  of  the  cost  of  the  building.  This  figure  is  for 
good  materials  and  labor,  and  of  course  is  subject  to  con¬ 
siderable  variation.  For  an  ordinary  house,  costing  from 
$1,500  to  $3,000,  the  cost  of  plumbing  may  be  taken  as  about 
8  per  cent,  for  moderate-priced  fixtures  and  public  sewer 
service.  The  cost  of  labor  alone  will  average  about  |  the 
cost  of  the  materials. 

Gas-Fitting.— The  cost  of  gas-fitting  may  be  approximately 
figured  as  about  3  per  cent,  of  the  cost  of  the  building. 
The  cost  of  labor  alone  varies  from  about  i  to  f  the  cost  of 
materials.  The  better  the  grade  of  fixtures,  the  lower  will 
be  the  ratio — provided  there  is  no  excessive  ornamentation, 
requiring  much  time  to  put  in  place — as  the  cost  of  the  labor 
is  about  the  same  for  cheap  fixtures  as  for  more  costly  ones. 

Heating.— The  cost  of  hot-air  installation  is,  approximately, 

5  per  cent,  of  the  cost  of  the  building ;  for  steam  heating, 

8  per  cent.;  for  hot- water  heating,  10  per  cent. 

In  estimating  on  heating  by  furnace,  the  average  cost  of 
labor  is  about  |  that  of  materials.  In  steam  and  hot-water 
heating,  the  ratio  is  about  5. 


362  ELEMENTS  OF  ARCHITECTURAL  DESIGN. 


Ha  dware. — Hardware  is  best  estimated  by  noting  the  quan¬ 
tities  required  for  each  portion  of  the  work  as  it  is  being 
measured,  afterwards  making  these  items  into  a  separate 
hardware  bill.  Many  of  the  articles,  as,  for  example,  the 
number  of  fixtures  for  doors  or  window  trimmings,  may  be 
readily  counted  from  the  plans.  Hardware  for  windows, 
doors,  etc.,  are  sometimes  included  in  estimating  the  cost  per 
window,  door,  etc.,  and  are  not  considered  separately.  The 
cost  of  hardware  depends  entirely  on  the  class  of  work  and 
finish  desired,  and  the  best  way  to  estimate  on  it  is,  after 
making  the  schedule,  to  select  suitable  designs  and  figure  the 
prices  from  a  catalogue.  An  approximate  estimate  for  ordi¬ 
nary  buildings  is  li  per  cent,  of  the  cost  of  the  building. 
From  15  to  20  per  cent,  of  the  cost  of  hardware  will  pay  for 
the  putting  in  place. 


ELEMENTS  OF  ARCHITECTURAL 

DESIGN. 


PROPORTIONS  OF  THE  GREEK  AND 
ROMAN  ORDERS. 

In  proportioning  the  Greek  and  Roman  orders,  a  uniform 
standard  of  measurement  was  adopted,  so  that  the  several 
parts  of  the  order  might  be  arranged  in  perfect  ratio.  This 
standard  consists  of  modules  and  parts.  A  module  is  the  semi- 
diameter  of  the  column,  measured  at  the  base,  and  each 
module  is  divided  into  30  equal  parts.  Each  diameter,  there¬ 
fore,  is  equal  to  2  modules,  or  00  parts. 


THE  GREEK  ORDERS. 

In  Fig.  1  is  shown  a  diagram  of  the  Greek  orders,  aftef 
measured  drawings  by  acknowledged  authorities,  drawn  to  a 
uniform  altitude.  A  is  an  example  of  pure  Doric,  from  the 
Portico  of  the  Parthenon,  at  Athens.  B  is  the  Ionic,  and 
is  taken  from  the  North  Porch  of  the  Erechthcum,  while  C  is 


GREEK  AND  ROMAN  ORDERS. 


363 


the  Corinthian,  after  the  monument  of  Lysicrates.  In  each 
example  a  is  the  stylobate  or  base,  b  is  the  column,  and  c  the 
entablature.  The  column  of  the  Doric  consists  of  a  shaft  and 
capital,  the  shaft  resting  directly  on  the  stylobate,  while 
the  columns  of  the  Ionic  and  Corinthian  have  a  base,  shaft, 
and  capital.  The  entablature  of  each  order  has  three  divi¬ 
sions — the  architrave,  frieze,  and  cornice. 


A  comparative  statement  of  the  relative  values  of  the  divi¬ 
sions  of  each  of  the  Greek  orders  is  given  in  Table  I,  and  is 
based  on  the  module,  or  semi-diameter,  as  the  unit  of  measure¬ 
ment  ;  as  previously  explained,  a  part  is  &  of  this  unit. 


Greek  Orders. 


364 


ELEMENTS  OF  ARCHITECTURAL  DESIGN. 


•mnnipo  omi 
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Height  of  Entablature. 

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a 

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jCornice. 

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Arch. 

9 

ft 

ci|cnoHr  ^|c» 

(M  O  CM 
rH  CM  CM 

m.  J 

rH  rH  rH 

Height  of  Column. 

: 

Total. 

ft 

o  o  o 

m. 

rH  CO  O 
rH  rH  C4 

ft, 

<3^ 

O 

ft 

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Base. 

d 

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a 

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Title. 

Doric . 

Ionic . 

Corinthian . 

d  2 

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GREEK  AND  ROMAN  ORDERS. 


365 


THE  ROMAN  ORDERS. 

The  Romans  adopted  the  column  and  beam  system  of  the 
Greeks,  and  joined  to  it  the  arch  and  vault.  The  union  of  the 
two  elements  of  arch  and  beam,  is  the  keynote  of  the  Roman 
style.  In  this  style  the  orders  were  used  more  for  decoration 
than  for  construction,  and  were  superposed,  or  set  one  upon 
the  other,  dividing  the  buildings  into  stories. 

The  five  Roman  orders  are  shown  in  Fig.  2.  A  is  the 
Tuscan;  B ,  the  Doric;  C,  the  Ionic;  D,  the  Corinthian;  and 
E,  the  Composite.  In  each  of  these,  a' ,  b',  and  c'  represent 


the  pedestal,  column,  and  entablature,  respectively.  For 
comparison,  the  relative  values  ot  the  lov  er  diameters  o  e 
shafts,  when  the  orders  are  profiled  to  a  uniform  total  heig  1 
of  31  ft.  8  in.,  is  given  in  Table  II. 

x 


366  ELEMENTS  OF  ARCHITECTURAL  DESIGN. 

TABLE  II. 

Roman  Oedebs. 


With  Uniform  Altitude  =  Sift.  8  in. 


Title. 

Index  Letter 

on  Fig.  2. 

Lower  Diameter 
of  Shaft. 

With 

Pedestal. 

Without 

Pedestal. 

Tuscan  . 

A 

to 

» 

h-4 

o 

AH 

3  ft.  7/s  in. 

Doric  . 

B 

2  ft.  6  in. 

3  ft.  2  in. 

Ionic  . 

C 

2  ft.  2*  in. 

2  ft.  9|  in. 

Corinthian  . 

D 

2  ft.  0  in. 

2  ft.  6|  in. 

Composite . 

E 

2  ft.  0  in. 

2  ft.  Of  in. 

Table  III  gives  the  relative  measurements,  with  respect  to 
the  module,  or  semi-diameter  of  the  shaft,  for  proportioning 
the  Roman  orders,  and  is  valuable  for  consultation  when 
preparing  preliminary  designs,  the  reference  letters  being 
those  shown  in  Fig.  2.  _ 


NOTES. 

In  connection  with  the  Roman  orders  it  is  well  to  keep  in 
mind  that  the  pedestal  is  one-third,  and  the  entablature  one- 
fourth,  the  height  of  the  column  in  all  cases. 

To  find  the  semi-diameter  of  the  column  in  any  order, 
divide  the  height  to  be  occupied  by  the  number  of  modules 
in  the  given  order.  Thus,  if  the  given  height  is  23  ft.  9  in. 
and  the  order  is  the  Ionic,  with  the  pedestal,  the  semi¬ 
diameter,  or  module,  will  be  23  ft.  9  in.  -4-  28£  —  10  in.;  if 
without  the  pedestal,  the  module  will  be  23  ft.  9  in.  -h  22£ 
=  12f  in.  The  lower  one-third  of  the  columns  is  cylindrical, 
the  upper  two-thirds  being  diminished  by  a  conchoidal  curve 
called  the  entasis,  the  reduction  of  the  shaft  at  the  neck  in 
all  cases  being  one-sixth  of  the  lower  diameter. 

In  terms  of  the  lower  diameter,  the  Tuscan,  Doric,  Ionic, 
Corinthian,  and  Composite  columns  are  respectively  7,  8,  9, 
10,  and  10  diameters  high. 


Roman  Orders. 


GREEK  AND  ROMAN  ORDERS. 


367 


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Title. 

Tuscan  . 

Doric  . 

Ionic  . 

Corinthian... 

Composite... 

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sturdy  than  those  of  the  Greek  prototype  and  the  shaft  is  often  left  unfluted.  The  Ionic  order  is 
more  enriched  than  the  Greek,  and  the  capital  is  generally  made  uniform  on  all  sides  by  placing 
the  volutes  anglewise.  The  Corinthian  order  was  the  favorite  of  the  Romans,  and  was  used  in 
the  largest  temples.  The  Composite  order  was  invented  by  the  Romans.  The  capital,  its  dis¬ 
tinctive  feature,  is  a  combination  of  the  Ionic  and  Corinthian. 


368  ELEMENTS  OF  ARCHITECTURAL  DESIGN. 


DRAWING  THE  ENTASIS  OF  A  COLUMN. 

The  shafts  of  classic  columns  have  a  curved  outline  called 
the  entasis.  In  the  Roman  orders  the  lower  third  is  straight 

and  vertical,  and  the  upper  two-thirds 
is  curved.  The  shaft  of  the  column  is 
diminished  one-sixth  9f  its  diameter  at 
the  neck.  Fig.  3,  representing  the 
curved  portion  of  the  shaft  of  an  Ionic 
column,  shows  a  method  for  profiling 
the  column.  Draw  the  center  line  a'  b', 
and  the  base  line  m'  b also,  the  upper 
line  k  a',  representing  the  neck  of  the 
shaft,  at  a  distance  of  11  modules  above 
in'  b',  making  its  length  equal  to  the 
semi-diameter  of  shaft  on  that  line, 
which  is  25  parts.  With  b'  as  a  center, 
and  a  radius  of  1  module,  describe 
the  arc  m'w';  through  k  draw  a  line 
parallel  to  a'  b',  intersecting  the  arc  at 
l'.  Divide  the  arc  m'V  into  11  equal 
parts,  as  shown  at  1,  2,  3,  etc.;  also, 
divide  a' b'  into  11  equal  parts  and 
draw  horizontal  lines  l\w',  %iv',  etc. 
From  point  1  on  the  arc,  draw  a  line 
parallel  to  a'b';  its  intersection  with 
the  line  1\  w'  will  give  one  of  the 
required  points.  From  2  draw  a  simi¬ 
lar  line  to  2U  etc.  All  the  points  being 
marked,  draw  a  curve  through  them 
by  means  of  a  spline,  or  flexible  strip. 

To  draw  the  lines  of  the  fluting  of  the  upper  portion  of  the 
shaft,  proceed  as  follows :  From  points  a',  n',  and  o'  in 
Fig.  3,  with  radii  equal  to  the  semi-diameter  of  the  shaft  at 
the  section  on  which  these  points  are  located,  describe 
quadrants.  As  the  Ionic  shaft  has  20  flutes,  divide  each 
quadrant  into  5  equal  spaces  of  18°  each  by  means  of  the 
protractor ;  from  these  points,  which  will  be  the  centers  of  the 
flutes,  with  a  radius  equal  to  %  of  the  length  of  arc  between 
the  centers  of  the  flutes,  describe  the  semicircles  defining  the 


k 


a 


101 


Ox 


v 


V 


V 


'C 


'■'O 


n 


o' 


t 


MOLDINGS. 


369 


flutes.  Project  the  lines  of  the  fillets  between  the  flutes  to 
their  position  on  the  horizontal  lines  k  a',  etc.,  by  drawing 
lines  parallel  to  the  center  line  a'  b',  and  through  the  three 
points  established  for  the  edge  of  each  flute  draw  a  curved 
line  by  means  of  a  spline. 


MOLDINGS. 


GREEK  MOLDINGS. 

The  outlines  of  the  Greek  moldings  follow  the  curves  of  the 
conic  sections — the  parabola,  hyperbola,  and  the  ellipse  and 
but  rarely  the  circle.  The  Roman  moldings  are  nearly 
always  formed  of  circular  arcs,  and  for  this  reason  lack  the 
delicacy  and  refinement  that  characterize  the  details  of  the 
Grecian  monuments. 

Greek  moldings  may  be  divided  into  three  classes,  accoid- 
ing  to  the  number  of  curves  composing  their  outlines.  In  the 
first  class  are  the  following : 

The  ovolo,  echinus ,  or  quarter-round  is  shown  at  (a)  Fig.  4. 
The  point  6,  direction  of  the  axis  ax,  and  the  coordinates  d  a 
and  a  b,  must  be  determined  before  the  curve— which  is  part 
of  a  hyperbola — can  be  traced.  Divide  a  b  and  b  c  into  the  same 
number  of  equal  parts,  and  take  the  point  x  anywhere  on  the 
line  ax — generally  at  a  distance  of  from  one  to  three  times 
ad  from  d,  according  to  the  curve  required.  Draw  lines  as 
shown,  and  trace  the  curve  through  the  intersections.  It  is 
well  to  assume  a  point  o  through  which  the  curve  must  pass, 
and  draw  a  line  from  3  through  o,  thus  fixing  the  point  x. 

The  cavetto  or  cove  (b)  is  one-quarter  of  an  ellipse.  Let  a  c 
and  a  b  be  the  required  height  and  depth  for  the  cove  b  c. 
Draw  the  large  semicircle  c  e  with  a  radius  equal  to  ac,  and 
the  small  semicircle  b  g  with  a  radius  equal  to  a  b.  Draw  any 
radius,  as  a,  g,  e.  From  g  erect  a  perpendicular,  and  nom  - 
draw  a  horizontal  line  intersecting  at  d,  a  point  on  the  ellipse. 

Other  points  may  be  similarly  found. 

The  scotia  (c)  is  also  an  elliptic  curve,  having  axes  inclined 
to  the  vertical ;  it  may  be  drawn  as  shown  for  the  cavetto. 


370  ELEMENTS  OF  A  R  (Jill TE C T  UFA L  DESIGN. 


The  toms  (d)  is  also  part  of  an  ellipse,  in  which  two  points 
d  and  c  are  given,  through, which  the  ellipse  must  pass.  Draw 
e  h  at  any  desired  inclination  through  d.  With  any  point  as  a 
as  a  center  describe  a  semicircle  passing  through  d.  Draw 
c m  perpendicular  to  eh;  cn  parallel  to  e h,  and  amn  cutting 


cn  at  n.  Then  the  large  circle  must  pass  through  n.  With  a 
as  a  center,  and  a  n  as  a  radius,  draw  the  outside  circle,  and 
complete  the  ellipse  as  before  shown. 

In  the  second  class,  composed  of  two  curves,  are  the 
following: 


MOLDINGS . 


371 


The  cyma  recta,  shown  at  (e),  is  often  made  up  of  two  arcs 
of  parabolas.  Make  a  b  equal  to  the  required  height,  also  a  e 
and  be,  each  equal  to  one-half  of  the  required  depth.  Divide 
ad,  a e, b d,  and  be  into  the  same  number  of  equal  parts. 
Draw  parallels  to  a  b ;  also,  the  lines  radiating  from  c  and  e, 
as  shown.  The  curves  may  then  be  traced  through  the  inter¬ 
sections.  This  molding,  when  more  deeply  cut,  is  sometimes 
made  up  of  two  reversed  arcs  of  ellipses. 

The  cyma  reversa  (/)  is  often  formed  of  reversed  elliptic 
arcs.  The  inclination  of  the  axis  a  b  may  be  taken  to  suit  the 
curve  required.  Through  d  draw  d  c  perpendicular  to  a  b  ; 
with  dc  as  a  semimajor  axis,  and  any  suitable  length,  as  ch, 
as  a  semiminor  axis,  draw  the  quarter  ellipse  d  h.  Through  e 
draw  ef  parallel  to  d  c,  giving  /  as  the  center  of  the  second 
ellipse.  With  /  as  center,  and  fli  and  fie  as  radii,  draw  the 
inside  and  outside  circles,  and  complete  the  curve  with  the 
quarter  ellipse  h  e. 

The  third  class  of  moldings  are  those  consisting  of  three 
curves,  and  are  generally  made  up  of  arcs  of  circles  combined 
with  arcs  of  ellipses.  The  bird’s-beak  molding,  shown  at  g, 
belongs  to  this  class.  The  principal  curve  cad  is  an  arc  of  a 
hyperbola.  The  arcs  of  the  circles  fk  and  ke  have  their 
centers  on  the  line  k  g,  and  are  tangent.  The  arc  fim  is  a 
quarter  ellipse. 

Accessory  moldings  which  may  be  used  in  connection  with 
an  the  forms  described  are  the  fillet,  which  is  the  simple 
square  band  shown,  crowning  the  cavetto  in  (6),  and  the 
bead,  which  is  the  small  rope-like  molding,  rather  more  than 
a  semicircle  in  section,  shown  at  the  base  of  the  ovolo  (a). 


ROMAN  MOLDINGS. 

The  Roman  moldings  are  almost  invariably  profiled  to  the 
arc  of  a  circle  or  of  two  tangent  circles. 

While  the  Greeks  relied  for  effect  on  the  graceful  contom 
of  their  moldings,  the  Romans  counted  more  upon  the  rich¬ 
ness  of  carved  ornament.  Delicacy  of  execution  in  the 
Greek  workmanship  gave  place  to  the  mechanical  and  osten¬ 
tatious  in  the  decoration  of  Roman  moldings.  Besides  this, 


372  ELEMENTS  OF  ARCHITECTURAL  DESIGN. 


the  execution  of  Roman  moldings  was 
often  very  careless.  As  a  general  rule, 
the  lines  of  enrichment  or  carving  on 
both  Greek  and  Roman  moldings  corre¬ 
sponded  to  the  profile  of  the  surface  on 
which  it  was  carved. 

The  torus,  shown  at  (a),  Fig.  5,  is  semi¬ 
circular,  the  center  being  at  c,  the  middle 
point  of  the  line  a  b. 

The  cavetto  or  cove,  shown  at  ( b ),  is  a 
concave  molding  whose  profile  is  a  quarter 
circle.  The  center  a,  is  found  by  extend¬ 
ing  the  lines  d  c  and  b  a  until  they  intersect. 

The  ovolo,  echinus,  or  quarter-round, 
shown  at  (c),  is  a  convex  molding  with  a 
quarter-circle  profile,  the  center  d  being 
found  as  shown. 

The  cyma  recta,  shown  at  (d),  is  made 
up  of  two  quarter  circles  tangent  at  e. 
The  centers  /  and  g  are  found  by  bisect¬ 
ing  the  lines  c  a  and  b  d. 

The  cyma  reversa,  shown  at  (e),  is  the 
reverse  of  the  cyma  recta,  which  is  con¬ 
cave  above  and  convex  below,  while  the 
former  is  convex  above  and  concave 
below.  The  drawing  explains  itself. 

The  scotia,  shown  at  (/),  is  drawn  as 
follows :  Having  given  the  points  c  and  d, 
draw  cd,  and  bisect  cd  at  e.  With  e  as 
center  and  e  c  as  a  radius  draw  a  semicircle 
dfc.  Draw  d  g  at  an  angle  of  30°  with  the 
base  fillet,  cutting  the  arc  at  g.  Erect  a 
perpendicular  at  d,  and  with  g  as  a  center 
and  a  radius  gd  cut  the  perpendicular 
at  h.  Draw  g  h  and  drop  a  perpendicular 
from  c,  cutting  ghatb.  With  b  as  a  center 
and  be  as  a  radius,  draw  the  arc  cjg. 
With  h  as  a  center  draw  the  arc  gid, 
completing  the  curve. 


Fig.  o. 


INDEX. 


Acetylene,  319. 

Air,  Flow  of,  316. 

Ancliors,  198. 

Angles  by  steel  square,  61. 
by  2'  rule,  60. 

Laying  out,  60. 
Measurement  of,  23. 

To  bisect,  55. 

Properties  of  steel,  85,  86. 
Radii  of  gyration  of, 91, 92, 93. 
Arc,  Center  of  circular,  56. 
Arches,  155,  200. 

Architectural  design,  362 
Areas,  Irregular,  36. 

of  circles,  44. 

Arithmetic,  1. 

Ashlar,  Data  on,  331. 

masonry,  182. 

Avoirdupois  weight,  23. 

Axis,  Neutral,  75. 


Board  measure,  335. 

Boiler  connections,  295. 
Boilers,  Kitchen,  294. 
Proportioning  parts  of,  306. 
Size  of,  305. 

Size  of  galvanized,  294. 

Bolts  and  nuts,  139. 

and  tension  bars,  138. 

Bonds  in  brickwork,  187. 
Brass  pipes  and  nipples,  270. 
Brick,  163. 

Sizes  of,  164. 

Strength  of,  73. 

Brickwork,  Bonds  in,  187. 
Data  on,  333. 

Estimating,  332. 

Building  materials,  Specific 
gravity  of,  30. 

Weight  of,  62. 

Buildings,  Cost  of,  per  cu.  ft., 
328. 


Baldwin’s  Rule,  301. 

Balloon  framing,  221. 

Bars,  Bolts  and  tension,  138. 
Basins,  Wash,  280. 

Bastard  sawing,  215. 

Baths,  Dimensions  of,  277 
Beams  and  girders,  106. 
Calculation  of,  115. 

Loads  on  wooden,  116. 
Rolled-steel,  118. 

Stone,  119. 

Theory  of,  107. 

Wooden,  115. 

Bearing  value  of  rivets,  130. 
Bedsteads,  Dimensions  of,  250. 
Bending  moment,  111,  113. 
Bevels,  Hopper,  248. 

Blinds,  342. 


ALCULATING  WEIGHT  OF 

Castings,  42. 

alculation,  Signs  used  in,  1. 
aps,  198. 

arpentry,  335. .  # 
arpentry  and  joinery,  208. 


joints,  217. 

Casings,  342. 

Castings,  Calculating  weight 
of/42. 

Cast-iron  columns,  98. 
iron  columns,  Design  of,  99. 
iron  columns,  Inspection  of, 


i-W*  .  . 

iron  columns,  Strength  of, 

101. 

iron  soil  pipes,  269. 


373 


374 


INDEX. 


Cements,  165. 

Strength  of,  73,  166. 

To  test,  165. 
walks  and  floors,  195. 

Center  of  gravity,  75. 
Cesspools,  274. 

Chairs  and  seats,  249. 
Channels,  Properties  of,  84. 
Cheek-cut  for  rafters,  227. 
Chimneys  and  fireplaces,  192. 
Church  dimensions,  231. 
Circle,  37. 

through  three  points,  56. 
Circles,  Table  of,  44. 

Circular  ring,  41. 
Circumferences  of  circles,  44. 
Cistern  filters,  293. 

Cisterns,  292. 

Closet  cisterns,  284. 
ranges,  282. 
seats,  282. 

Closets,  pan  and  plunger,  280. 
Siphon,  281. 

Washout,  281. 

Water,  280. 

Coal  gas,  318. 

Coefficients  of  elasticity,  69. 
Columns,  94. 

Cast-iron,  98. 

Design  of  cast-iron,  99 
Entasis  of,  368. 

Inspection  of  cast-iron,  100. 
Strength  of,  94. 

Strength  of  round  cast-iron, 
102. 

Strength  of  square  cast-iron, 

101. 

Strength  of  steel,  103. 
Strength  of  wooden,  97. 
Structural-steel,  106. 
Wooden,  95,  96. 

Common  fractions,  2. 
Concrete,  168. 

Cone,  40. 

Connections,  Radiator,  310. 
Cornices,  Plaster,  355. 

Cube  root,  8,  10. 

roots,  Square  and,  13. 

Cubic  measure,  23. 

Curved  roof,  Rafters  for,  228. 
Cylinder,  39. 

To  develop,  60. 


Dead  Loads,  62. 

Decay,  Prevention  of,  233. 
Decimal  fractions,  4. 
of  a  foot,  53. 
of  an  inch,  53. 

Deflection,  113,  114. 

Design,  Architectural,  362. 
of  riveted  girders,  120. 
of  roof  trusses,  149. 
of  structural-steel  columns, 
106. 

Structural,  62. 

Diagrams,  Frame  and  stress, 
141. 

Direct  radiators,  303. 

Disposal  of  sewage,  274. 

Door,  Cost  of,  344. 
frames,  343. 
frames,  Cost  of,  343. 

Doors,  239. 

Butts  for,  241. 

Construction  of,  240. 

Fitting,  241. 

Framing,  240. 

Proportions  of,  239. 
Drainage,  Inspection  and  test¬ 
ing,  275. 
system,  269. 

Drawing,  Geometrical,  55. 

Dry  measure,  24. 
Duodecimals,  6. 

Efflorescence,  191. 
Elasticity,  Modulus  of,  69. 
Ellipse,  38,  57. 

Entasis  of  col”,mn,  368. 
Equivalent  irnals  of  foot, 
53. 

decimals  of  inch,  53. 
Estimates,  Approximate,  328. 
Estimating,  328. 

Evolution,  8. 

Exhaust-steam  heating,  307. 

Factor  of  Safety,  70. 

Fall  for  drain  pipes,  274. 
Ferrules,  Brass,  271. 

Weight  of  brass,  271. 

Filters,  Cistern,  293. 

Fink  roof  truss,  147. 
Fireplaces,  193. 


INDEX. 


375 


Fireproof  floors,  Weight  of,  64. 

material,  65. 

Fittings,  Pipes  and,  269. 
Fixtures,  Plumbing,  277. 
Flagpoles,  232. 

Flange  plates,  Length  of,  125. 
Flanges,  123. 

Floor  connections,  283. 

Cost  of  finished,  340. 
Flooring,  Estimating,  337. 
Floors  and  walks, Cement,  195. 
Weight  of,  63. 

Weight  of  fireproof,  64. 

Flow  of  air,  316. 

of  gas,  321. 

Fluxes,  296. 

Footings  and  foundations,  171. 
Proportioning,  172. 

Spread,  175. 

Forced  ventilation,  316. 
Forces,  Parallelogram  of,  140. 
Polygon  of,  140. 

Resolution  of,  141. 

Triangle  of,  140. 

Formulas,  31. 

Foundations,  Footings  and, 
171. 

Thickness  of,  178. 

Fourth  root,  12. 

Fractions,  Common,  2. 
Decimal,  4. 

Frame  and  stress  diagram,  141. 
Frames,  Door  and  window, 
341,  343. 

Framing,  Balloon,  221. 

Roof,  226. 

Sizes  of,  225. 

Furnace  heating,  312. 
Furniture,  Dimensions  of,  249, 
250. 


Galvanized  Boilers,  Size 
of,  294. 

Gambrel  roof,  229. 

Gas,  Acetylene,  319. 
and  gas-fitting,  318. 

Coal,  318. 
fitting,  325. 
fitting,  Cost  of,  361. 
fitting,  Gas  and,  318. 

Kinds  of,  318. 


Gas  meters,  323. 

Oil,  318. 

Pressure  of,  320. 

Producer,  318. 

Water,  318. 

Geometrical  drawing,  55. 
Girders,  Beams  and,  106. 
Design  of  riveted,  120. 
Flange  plates,  125. 

Flanges  of,  123. 

Rivet  spacing,  127. 

Stiffeners  for,  122. 

Gravel  roofing,  354. 
roofs,  255. 

Gravity,  Center  of,  75. 

Greek  and  Roman  orders,  362. 

moldings,  369. 

Gutters,  256. 

Gyration,  Radius  of,  81. 


Hangers,  198. 

Hardness  of  woods,  213 
Hardware,  362. 

Heating  and  ventilatic  300. 
Cost  of,  361. 

Exhaust-steam,  307. 
Furnace,  312. 

Hot-water,  308. 

Steam,  300. 

Helix,  39,  59. 

Hemlock,  cost  per  M,  340. 
Hexagon,  To  construct  a,  56. 
Higher  roots,  12. 

Hip  or  valley  rafters,  227,  228, 
Hopper  bevels,  248. 

Hoppers,  280. 

Ilot-water  heating.  308. 

Howe  roof  truss,  143. 
Hydraulic  ram,  291. 
Hyperbola,  58. 


I  Beams,  Properties  of,  90. 
Illumination  required,  325. 
Indirect  radiators,  304. 
Inertia,  Moment  of,  77. 
Inspection  of  cast-iron  col¬ 
umns,  100. 
of  drainage,  275. 

Involution,  7. . 

Iron  (see  cast  iron). 


INDEX. 


376 


Jack-Rafters,  227,  228. 
Joinery,  237. 
and  carpentry,  208. 
Data  on,  342. 
Estimating,  341. 
Joints  in,  237. 

Joints,  Carpentry,  217. 
in  joinery,  237. 

Kitchen  Boilers,  294. 
Sinks,  Sizes  of,  287. 


Lathing,  258. 

Estimating,  357. 

Latrines,  282. 

Laundry  tubs,  289. 

Lead  pipes,  272. 

pipe  tacks,  Spacing  of,  299. 
Lime,  104. 

Linear  measure,  22. 

Line  equal  to  any  arc,  56. 
of  pressure,  156*. 

Parallel,  55. 

To  divide  a,  55. 
lines  and  plane  surfaces,  35. 
Liquid  measure,  24. 

Live  loads,  65. 

Load,  113. 

Maximum,  113. 

Loads,  Dead,  62. 
for  wooden  beams,  116. 
Live,  65. 

on  structures,  62. 

Snow  and  wind,  67. 

Long  ton  table,  23. 


Mains  and  Branches,  311. 
Masonry,  162. 

Ashlar,  182. 

Construction,  180. 

Effect  of  temperature  on,  188. 
Estimating,  329. 

Rubble,  182. 

Specific  gravity  of,  30. 
Stone,  182. 

Strength  of,  74. 

Strength  of  materials,  73. 
Materials,  Plastering,  259. 
Quantities  of,  169. 

Strength  of,  68. 


Materials,  Set  per  day,  337. 
Maxims,  Sanitary,  265. 
Maximum  bending  moment, 
113. 

load,  113. 

Measures,  Weights  and,  22. 
Mensuration,  35. 

Metals,  Specific  gravity  of,  29. 

Strength  of,  70. 

Meters,  Gas,  323. 

Metric  areas,  26. 
capacity,  27. 
length,  26. 
system,  25. 
volumes,  26. 
weights,  27. 

Miscellaneous  notes,  361. 
table,  25. 

Miter  bevel  for  stringer  cut, 
247.  ' 

cuts  for  purlins,  228. 
Modulus  of  elasticity,  69. 
of  rupture,  70. 

Section,  82. 

Moldings,  369. 

Greek,  369. 

Roman,  371. 

Mold,  Raking,  248. 

Moment,  Bending,  111,  113. 
Moment  of  inertia,  77. 
of  inertia,  Graphical 
method,  79. 

Resisting,  114. 

Moments,  106. 

Mortar,  167. 

Mortars,  Tensile  strength  of 
cement,  166. 


Nails,  Estimating,  338. 
Natural  ventilation,  315. 
Neutral  axis,  75. 

Nipples,  Solder,  270. 
Nuts,  Bolts  and,  139. 


Octagon  Inscribed  in 
Square,  57. 

Orders,  Greek,  362,  364. 
Proportions  of,  362. 
Roman,  365,  366. 


INDEX. 


377 


Paint,  Cost  of,  359. 

Painting  and  papering,  357. 

quantities,  357. 

Pan  and  plunger  closets,  280. 
Paneling,  Estimating,  343. 
Papering,  360. 

Parabola,  58. 

Parallelogram,  36. 

of  forces,  140. 

Partitions,  Weight  of,  63. 
Perpendicular,  To  draw  a,  55. 
Piles,  176. 

Pins,  Resisting  moments  of, 
137. 

Shearing  and  hearing  val¬ 
ues  of,  137. 

Strength  of,  133. 

Pipe,  Length  of  wiped  joints 
for  lead,  300. 

tacks,  Spacing  of  lead,  299. 
Pipes  and  fittings,  269. 
Capacity  of  gas,  326. 
Cast-iron,  269. 

Fall  for  drain,  274. 

Hot-air,  313. 

Lead,  272. 

Size  of  gas,  325. 

Size  of  steam,  302. 

Size  of  water,  293. 

Sizes  of,  272. 

Sizes  of  street  service,  290. 
Weight  of,  269. 

Piping,  302,  309. 

Radiator,  309. 

Pitch  of  rivets,  133. 

Pitches  for  gambrel  roof,  229. 
Plank  truss,  229. 

Plastering,  258. 
costs,  356. 

Estimating,  354. 
materials,  259. 
quantities,  356. 

Plates,  Length  of  flange,  125. 
Plumbers’  tables,  296. 
Plumbing,  265. 

Cost  of,  361. 
fixtures,  277. 

Plunger  and  pan  closets,  280. 
Polygon,  36. 

Inscribed,  57. 
of  forces,  140. 

Pressure,  Line  of,  156. 


Pressure,  Measurement  of 
gas,  321. 
regulators,  324. 

Prism,  40. 

Prismoid,  41. 

Properties  of  sections,  75. 
Proportion  of  rooms,  232. 
Pumps,  290. 

Purlins,  Miter  cuts  for,  228. 
Pyramid,  40. 


Quarter  Sawing,  215. 


Radiating  Surface,  30S,  310. 
Proportion  of,  to  glass  sur¬ 
face,  301.  ,  ,, 

Proportion  of,  to  volume  of 
room,  301. 

Radiation,  300. 

Radiator  connections,  310. 

piping,  309. 

Radiators,  Direct,  303. 

Flue,  304. 

Indirect,  304. 

Prime  surface,  303. 

Tappings  for  prime  surface, 
303. 

Tappings  for,  309. 

Radii  of  gyration,  two  angles, 


91  92,  93. 

Radius  of  gyration,  81. 
Rafters,  Cheek-cut  for,  227. 
for  curved  roof,  228. 

Hip,  227. 

Hip  or  valley,  228. 

Jack-.  227. 

Lengths  and  cuts  of,  226. 
Raking  mold,  248. 
Reactions,  108. 

Ram,  Hydraulic,  291. 
Ranges,  Closet,  282. 
Registers,  Area  of,  314. 
Hot-air,  313. 

Regulators,  Pressure,  32o. 
Resisting  inches,  82. 

moment,  114. 

Resolution  of  forces,  141. 


Ring,  37. 


378 


INDEX. 


Risers  and  treads,  Proportions 
of,  247. 

Height  of,  312. 

Riveted  girders,  Design  of,  120. 
Rivet  spacing,  127. 

Rivets,  Pitch  of,  133. 

Shear  and  bearing  value  of, 
130. 

Strength  of,  128. 

Rolled-steel  beams,  118. 
Roman  and  Greek  orders,  362. 
Ionic  volute,  59. 
moldings,  371. 
orders,  365,  366. 

Roof  framing,  226. 
mensuration,  346. 
trusses  (see  trusses). 
Roofing,  250. 

Estimating,  346. 

Gravel,  354. 

Tin,  253. 

Roofs,  Gravel,  255. 

Tile,  354. 

Tin,  353. 

Weight  of,  63. 

Wind  pressure  on,  68. 
Rooms,  Acoustic  proportions 
of,  232. 

Proportions  of,  231. 

Roots,  Cube,  10. 

Fourth,  12. 

Higher,  12. 

Sixth,  12. 

Square,  8. 

Square  and  cube,  13. 

Round  cast-iron  columns,  102. 
Rubble  masonrv,  182. 
Rupture,  Modulus  of,  70. 


Safety  Factor,  70. 

Sand,  167. 

Sanitary  maxims,  265. 

Sash,  341. 

Sawing,  Quarter  and  bastard, 
215. 

Schoolrooms,  231. 

Seats,  Closet,  282. 

Vent,  283. 

Section  modulus,  82. 

Sections,  Properties  of,  75. 
Sector,  Circular,  37. 


I  Segments,  Circular,  38. 
of  circle,  57. 

Sewage,  Disposal  of,  274. 

Sewers,  Sizes  and  grade  of, 
272. 

Sheathing,  To  calculate,  336. 
Shear,  109. 

of  Rivets,  130. 

Sheet  Iron,  Weight  of,  299. 
Shingles,  Cost  of,  351. 
Estimating,  349. 

Number  required,  350. 

Siding  a  tower,  230. 

To  measure,  337. 

Signs  used  in  calculation,  1. 
Sinks,  286. 

Sizes  of,  287. 

Siphon  closets,  281. 

Sixth  root,  12. 

Slates,  Number  required,  352.  ! 
Slating,  250. 

Cost  of,  353. 

Estimating,  351. 

Snow  and  wind  loads,  67. 

Soils,  Bearing  capacity  of,  74.  ! 
Solders,  297. 

Solids  and  curved  surfaces,  > 
39. 

Specific  gravities  and  weights, 
29. 

Sphere,  41. 

Spiral,  58. 

Spread  footings,  175. 

Square  and  cube  roots,  13. 
cast-iron  columns,  101. 
measure,  22. 
root,  8. 

Steel,  234. 

Stairs,  Cost  of,  345. 

Stairways,  342. 

Notes  on,  247. 

Stable  dimensions,  232. 

Steam  heating,  300. 

Steel  (see  structural  steel), 
square,  234. 

Stiffeners,  122. 

Stone,  162. 
beams,  119. 

Cost  of,  331. 

Data  on  cut,  331. 
finishes,  184. 
masonry,  182. 


INDEX. 


379 


Stone,  Strength  of,  73. 
Stonework,  Estimating,  328. 

Notes  on,  180. 

Strain,  69. 

Street  service,  290. 

Strength  of  masonry  mate¬ 
rials,  73. 
materials,  68. 
metals,  70. 
rivets  and  pins,  128. 
timber,  71. 

Stress,  68. 

and  frame  diagrams,  141. 
Stresses,  Compressive  and  ten¬ 
sile,  146. 

in  roof  trusses,  142. 
Principles  of,  140. 

Stringer  cut,  Miter  bevel  for, 
247. 

Structural  design,  62. 
steel  columns,  103. 
steel  column,  Design  of,  106. 
Structures,  Loads  on,  62. 
Stucco  work,  Estimating,  355. 
Studs,  Number  of,  336. 

Surface,  Radiating,  308,  310. 
Surfaces,  Lines  and  plane,  35. 
Curved,  39. 

Surveyor’s  square  measure,  23. 


Tables,  250. 

(See  the  topic  in  question.) 
Tacks,  spacing  of  lead  pipe, 
299. 

Temperature,  Effect  of,  on 
masonry,  188. 

Tensile  strength  of  cement, 
166. 

Terra  cotta,  164. 

Testing  and  installation,  326. 

of  drainage,  275. 

Tile  roofs,  354. 

Timber,  Qualities  of,  213. 
Selecting,  214. 

Strength  of,  71. 

Tin  roofing,  253. 
roofs,  353. 

Tower,  Siding  a,  230. 
Trapezium,  36. 

Trapezoid,  36. 


Treads  and  risers,  Propor¬ 
tioning  of,  247. 

Triangle,  35. 

of  forces,  140. 

Troy  weight,  24. 

Truss,  Fink  roof,  147. 

Howe  roof,  143. 
plank,  229. 

Trusses,  Design  of  roof,  149. 
Roof,  140. 

Stresses  in  roof,  142. 

T  shapes,  Properties  of,  87,  88. 
Tubes,  Vertical,  303. 

Tubs,  Laundry,  289. 


Ultimate  Strength,  69. 
Urinals,  286. 


Ventilation,  314. 
Forced,  316. 

Heating  and,  300. 
Natural,  315. 

Vents,  Seat,  283. 
Verandas,  Cost  of,  346 
Volute,  Roman  Ionic,  59. 


Wainscoting,  342. 

Walks  and  floors,  Cement,  195. 
Walls,  Retaining,  206. 
Thickness  of,  178. 
Waterproofing,  191. 

Wash  basins,  280. 

Washout  closets,  281. 

Water  closets,  280. 
pipes,  Size  of,  293. 
supply  and  distribution, '290. 
Water  proofing  walls,  191. 

Web,  Proportioning,  120. 
Wedge,  41. 

Weight  (see  article  in  ques¬ 
tion). 

Weights  and  measures,  22. 

Specific  gravities  and,  29. 
Wind  and  snow  loads,  67. 
Window  frames,  Cost  of,  344. 
Windows,  242. 

Area  of,  242. 

Cost  of,  345. 

Construction  of,  244. 

Design  of.  242. 


380 


INDEX. 


Wind  pressure,  67. 

pressure  on  roofs,  68. 
Wooden  beams,  115. 
beams,  Loads  for,  116. 
columns,  95. 
columns,  Design  of,  96. 
Wood,  Imperfections  in,  215. 


Woods,  Hardness  of,  213. 
Specific  gravity  of,  31. 
used  in  building,  208. 
Wrought-iron  and  steel  pipes, 
269. 

Z  bars,  Properties  of,  89. 


The  International  System 

OF 

EDUCATION 

BY  MAIL 

• - 

• 

The  method  of  correspondence  instruction  in  the  indus¬ 
trial  sciences  of  the  International  Correspondence  Schools 
was  originated  in  1891,  by  Thomas  J.  Foster,  President  of 
the  Schools,  and  was  first  used  in  the  Correspondence 
School  of  Mines. 


Distinctive  Features  of  the 
International  System 

1.  Courses  of  Instruction  for  particular  occu¬ 
pations,  in  which  only  such  facts,  processes,  and 
principles  are  taught  as  are  necessary  to  qualify 
the  student  therein. 

2.  Textbooks,  Question  Papers,  and  Drawing 
Plates,  prepared  for  each  Course;  Principles 
applied  in  examples  of  practical  value  to  the  stu¬ 
dent;  Frequent  Revision,  to  keep  pace  with  latest 
methods  in  trades  and  manufactures. 

3.  Thorough  examination  and  correction  of 
the  written  work  of  the  student,  and  full,  clear, 
and  exact  written  explanations  of  all  difficulties 
met  with  in  studying- 


ADMINISTRATION  BUILDINGS  OF 


International 
Correspondence  Schools 


Scranton,  Pa. 


Erected  in  1898 


650,000  Students  and  Graduates.  Faculty 
of  358  Professors  and  Assistants 


ESTABLISHED  1891 


THE  ORIGINAL 


Our  Standing  and  Responsibility 

The  International  Textbook  Company,  Proprietors  of  the 
International  Correspondence  Schools,  is  incorporated  under 
the  laws  of  Pennsylvania,  and  has  a  paid-up  capital  ot 
$3,000,000.  Its  administration  buildings  and  its  mammoth 
printery  and  instruction  building  were  erected  expressly  for 
the  purposes  of  correspondence  instruction,  at  a  cost  of  nearly 
a  million  dollars. 

The  administration  buildings,  two  in  number,  are  situated 
at  434-436  Wyoming  Avenue,  are  five  and  four  stories  high, 
respectively,  and  contain  the  business  departments  of  the 
Schools. 

The  printery  and  instruction  building  is  situated  at  the 
corner  of  Wyoming  Avenue  and  Ash  Street.  It  is  two  and 
three  stories  high,  and  contains  the  instruction,  illustrating, 
and  printing  departments  of  the  Schools. 

References 

We  refer  to  the  commercial  agencies,  or  to  any  bank  officer, 
teacher,  clergyman,  or  public  official  in  Scranton,  as  to  our 
responsibility  and  reputation.  We  will  repay  the  traveling 
expenses  of  any  person  or  committee  who  may  come  to 
Scranton  and  find  that  we  have  made  misrepresentations  as 
to  the  practicability  and  efficiency  of  our  method  of  instruc¬ 
tion  and  Courses  of  study,  or  as  to  our  financial  standing. 
We  will,  further,  refer  a  person,  intending  to  enroll,  to  a 
student  in  his  locality,  with  whom  he  may  correspond. 

From  J.  A.  Linen,  Esq. 

President  First  National  Bank,  Scranton,  Pa. 

This  Bank  ranks  third  in  the  roll  of  honor 
of  National  Banks  in  the  United  States 

We  regard  the  Schools  as  an  educational  institution  of  a 
very  superior  character.  The  officers  and  managers  are  men 
of  integrity  and  business  capacity,  and  stand  high  in  this 
community.  J*  LINEN* 


3 


System  of  Instruction 

Each  Course  is  made  up  of  a  series  of  Instruction  Papers, 
clearly  written  and  fully  illustrated.  When  the  student 
enrolls,  the  first  two  Instruction  Papers  are  sent  to  him. 
After  carefully  studying  the  first  Instruction  Paper,  he  writes 
his  answers  to  the  Examination  Questions  at  the  end  of  the 
Paper,  sends  his  work  to  the  Schools  for  examination  and 
correction,  and  continues  with  his  second  Paper.  When  the 
sets  of  answers  are  received  at  the  Schools,  they  are  care¬ 
fully  examined.  If  an  error  is  discovered,  it  is  not  only 
indicated  in  red  ink,  hut,  if  considered  advisable,  a  careful 
explanation  of  that  particular  problem  is  written  on  the  back 
of  the  sheet.  ’ 

Papers  are  passed  if  a  mark  of  90  per  cent,  has  been 
attained.  The  answers  are  then  returned,  accompanied  by  a 
Percentage  Slip  and  the  third  set  of  Papers.  The  student 
always  has  at  least  one  Paper  to  study  while  the  answers  to 
the  previous  Paper  are  being  examined  and  corrected. 

How  We  Teach  Drawing 

The  first  Instruction  Paper  on  Drawing  and  a  mailing  tube 
for  returning  the  finished  Plate  are  sent  to  the  student. 
Detailed  directions  are  given  for  the  use  of  instruments  and 
making  the  first  Plate.  Beginning  with  simple  lines,  the 
student  is  advanced  to  actual  working  drawings,  to  pen-and- 
ink  rendering,  to  drawing  from  nature,  from  cast,  and  from 
the  figure,  and  to  water-color  rendering. 

Special  Instruction 

When  a  student  desires  assistance  from  his  Instructors,  he 
uses  an  “Information  Blank”  provided  for  the  purpose.  When 
considered  necessary,  or  on  request,  a  “Special  Instructor”  is 
assigned  to  give  personal  attention  to  his  case,  until  the 
subject  is  completed.  A  Certificate  of  Progress  is  granted  on 
the  completion  of  each  Division  of  a  Course,  and  a  Certificate 
of  Proficiency,  or  Diploma,  is  awarded  when  the  student 
passes  his  final  examination. 


4 


Advantages  of  the  System 

1 .  You  Study  at  Home.— You  do  not  have  to  leave  home 
to  secure  the  education;  the  education  comes  to  you. 

2.  No  Time  Lost  From  Work. — You  can  keep  right  on 
With  your  work,  and  study  during  spare  hours.  This  is  the 
only  system  of  education  that  enables  the  student  to  com¬ 
bine  education  and  experience  by  immediately  using  in  his 
daily  work  the  knowledge  gained  through  his  studies. 

3.  You  Study  When  It  Is  Convenient. — Our  Schools 
never  close.  You  can  study  when  and  where  you  please. 
Failure  is  impossible  to  those  that  try. 

4.  We  Teach  Everywhere. — You  can  move  from  place 
to  place  while  studying.  \Ye  teach  wherever  the  mails  reach. 
We  have  students  in  every  country. 

5.  No  Books  to  Buy.— You  have  no  textbooks  to  buy. 
We  furnish  all  Instruction  Papers,  return  envelopes,  and 
information  Blanks.  We  prepay  all  postage  on  mail  sent  by 
us  to  the  student.  All  that  it  need  cost  you,  outside  of  the 
price  of  your  Course,  is  the  postage  on  matter  sent  to  us. 

6.  Instruction  Private.— Instruction  is  conducted  pri¬ 
vately.  None  need  know  you  are  a  student  except  ourselves. 

7.  Only  Spare  Time  Required.— Your  studies  need  not 
interfere  with  business  or  social  engagements. 

8.  Written  Explanations _ Written  explanations  are 

always  with  you,  and  can  be  studied  repeatedly. 

9.  Each  Student  a  Class  by  Himself.— Our  student’s 
written  examinations  enable  his  Instructor  to  detect  Aveak 
points  and  assist  him.  Each  student  is  a  class  by  himself, 
because  the  Instructor  attends  to  him  alone. 

10.  Study  Assures  Success. — The  successful  comple¬ 
tion  of  any  Course,  and  our  Diploma,  is  assured  to  all  that 
can  read  and  write  and  will  study  as  we  direct. 

1 1 .  Backward  Students  Assisted.— We  take  great  pains 
with  backward  students;  they  become  our  best  friends. 

12.  Prepared  for  Examinations.— Our  Courses  prepare 
the  student  for  examinations;  he  learns  to  express  himself 
clearly  in  writing,  and  remembers  what  he  writes. 

13.  Open  to  All.— Our  Schools  are  open  to  all— both 
sexes— “seven  to  seventy.” 


5 


Bound  Volumes  Furnished  to 
Students 

Realizing  the  great  value  of  the  Instruction  Papers  and 
Drawing  Plates  to  those  that  have  studied  them,  and  the 
desirability  of  preserving  them  for  reference,  the  Schools 
have  had  them  reprinted  and  bound  into  handsome  half¬ 
leather  volumes.  The  number  furnished  varies  from  one  to 


Bound  Volumes  of  the  Complete  Architectural 

Course 


ten  volumes,  according  to  the  Course  for  which  the  student 
enrolls.  He  has  the  use  of  them  as  long  as  he  lives  up  to  his 
contract.  Their  contents  correspond  to  the  set  of  the  Instruc¬ 
tion  Papers  and  Examination  Questions  sent  to  the  student 
throughout  his  Course,  and  are  supplied  in  addition  to  them. 
Each  set  gives  the  student  thorough  and  complete  instruc¬ 
tion  concerning  the  theory  and  practical  application  of  the 
principles  underlying  the  trade  or  profession  on  which  they 
treat.  Containing  as  they  do  the  complete  Course  in  perma¬ 
nent  form,  the  volumes  constitute  ail  unequaled  reference 
library,  available  at  all  times. 


6 


What  the 

International  Correspondence 
Schools  Are  Doing 


First — Teaching  Mechanics  the  Theory 
of  Their  Trades 

In  nearly  every  machine  shop,  drafting  room,  industrial 
plant,  etc.,  we  have  students  that  have  secured  promotion 
and  advances  in  salary  through  study  in  our  Schools.  The 
increased  value  of  an  employe  that  masters  the  theory  of  his 
trade  or  profession  brings  prompt  and  substantial  recognition. 

Experience  in  teaching  650,000  students  has  proved  that 
any  one  that  can  read  and  write  English  is  able  to  keep  right 
on  with  his  work,  and  at  the  same  time  acquire  a  technical 
education.  You  do  not  have  to  leave  home  or  quit  work. 
Our  prices  are  low,  our  payments  easy,  and  you  have  no 
textbooks  to  buy. 

If  you  are  dissatisfied  with  your  salary,  you  can  increase 
your  earning  capacity  by  study  at  home,  and  fit  yourself  for 
the  highest  positions  in  your  trade  or  profession. 


THROUGH  THIS  PLAN 


Machinists  and  Apprentices 
Firemen  and  Oilers 
Linemen  and  Electricians 
Carpenters,  Etc. 

Miners  and  Mine  Bosses 
Chainmen  and  Surveyors 
Tinsmiths 
Plumbers,  Etc. 

Assistant  Chemists 


Have  Become 
Have  Become 
Have  Become 
Have  Become 
Have  Become 
Have  Become 
Have  Become 
Have  Become 
Have  Become 


Mechanical  Draftsmen. 
Steam  Engineers. 
Electrical  Engineers. 
Architects  and  Builders. 
Foremen  and  Managers. 
Civil  Engineers. 

Pattern  Draftsmen. 
Sanitary  Engineers. 
Chief  Chemists. 


7 


What  the 

International  Correspondence 
Schools  Are  Doing 

Second — Helping  Misplaced  People  to 
Change  Their  Work 

The  man  that  would  succeed  as  an  electrical,  mechanical, 
or  civil  engineer,  or  architect  is  filling  a  iflO-a-week  position 
as  salesman  or  assistant  bookkeeper. 

The  woman  that  would  be  valuable  in  an  office,  drafting 
room,  or  laboratory  position  is  earning  a  poor  living  as  clerk, 
housekeeper,  or  seamstress. 

These  conditions  exist  because  people  do  not  know  of  any 
practical  plan  to  change  to  the  occupation  of  their  choice. 

We  have  solved  the  problem. 

We  have  qualified  hundreds  for  salaried  positions  in  new 
lines  of  work,  at  their  homes,  in  spare  hours,  and  at  small 
expense.  They  held  their  old  positions  until  they  changed 
to  the  new,  with  a  salary  better  than  before. 

They  are  now  earning  while  learning,  and  earn  more  as 
they  learn  more. 


THROUGH  THIS  PLAN 


Clerks, 

Salesmen, 

Bookkeepers, 

Women, 

Mechanics, 

Farmers, 

Laborers, 

Teachers, 

Telegraphers, 

Drivers, 


HAVE 

BECOME 


Draftsmen, 

Surveyors, 

Architects, 

Engineers, 

Chemists, 

Stenographers, 

Accountants, 

Ad  Writers, 

Window 

Dressers. 


8 


What  the 

International  Correspondence 
Schools  Are  Doing 


Third — Enabling  Young  People  to  Sup¬ 
port  Themselves  While  Learning 
Professions 


Young  men  or  women  obliged  to  earn  their  own  living 
are  not  debarred  from  a  successful  career  because  they  have 
not  the  time  or  means  to  attend  college.  By  our  method  of 
education  by  mail  they  can  qualify  at  home,  in  spare  time, 
and  at  small  cost,  for  minor  positions  and  rapidly  advance. 

A  few  months’  study  of  Mechanical  or  Architectural 
Drawing  with  us  will  qualify  young  men  for  positions  as 
assistant  draftsmen  in  machine  works  or  electrical  manu¬ 
factories,  or  with  architects.  Here  they  can  combine  study 
with  work,  and  advance.  Through  the  Surveying  and 
Mapping  Course  they  can  qualify  as  surveyors  on  engineer¬ 
ing  corps,  and  through  further  study  with  us  advance  to 
the  highest  positions. 

Those  that  desire  to  enter  on  business  life  can  qualify, 
through  our  instruction,  for  good  positions  as  bookkeepers  or 
stenographers,  ad  writers,  window  dressers,  etc. 


THROUGH  THIS  PLAN 


Men  J 


} 


Have  Become 


Draftsmen, 

Electricians, 

Surveyors. 


Young 

Women 


9 


The  School  of  Mechanical 
Engineering 

Mechanical  Course. — This  is  intended  For  all  those  that 
desire  a  thorough  knowledge  of  engineering  calculations, 
mechanical  drawing,  and  the  design  of  steam  engines,  boil¬ 
ers,  and  modern  machinery.  It  is  a  complete  treatise  on  the 
drafting-room  practice  of  mechanical  engineering. 

Mechanical  Engineering  Course.— This  is  intended  for 
machinists,  draftsmen,  machine  designers,  mechanical  engi¬ 
neers,  apprentices,  foremen,  superintendents,  etc.  This 
Course  comprises  a  thorough  and  exhaustive  treatment  of 
the  subject  of  mechanics,  supplemented  by  a  complete 
treatise  on  modern  shop  practice,  and  is  the  most  thorough 
Course  in  practical  mechanical  engineering  ever  published. 

Shop  Practice  Course. — This  is  divided  into  five  parts, 
as  follows:  Machine-Shop  Practice  is  intended  for  all  those 
that  wish  to  get  a  thorough  knowledge  of  modern  machine- 
shop  practice.  Toolmaking  is  intended  for  those  that  desire 
information  in  regard  to  the  latest  and  most  approved  tool¬ 
making  methods.  Patternmaking  covers  thoroughly  every 
branch  of  patternmaking.  Foundrywork  gives  thorough 
instruction  in  all  phases  of  foundrywork.  Blacksmithing 
and  Forging  is  intended  to  give  blacksmiths,  helpers,  etc.  a 
thorough  knowledge  of  the  best  methods  employed  in  their 
trade. 


Increased  Salary  Over  100  Per  Cent. 


Having  been  obliged  to  make  my 
own  way  before  I  had  a  chance  to  get 
a  practical  education,  I  soon  found 
that  the  man  with  the  working  educa¬ 
tion  got  the  pay,  while  the  others  got 
the  hard  work.  After  studying  from 
textbooks  and  at  night  schools  with 
but  little  success,  I  enrolled  in  the 
1. 0.  S.  Since  I  enrolled  I  have  secured 
better  employment,  and  my  pay  has 
been  increased  over  100  per  cent.  I 
am  now  first-class  machinist  for  the 
U.  S.  Government. 

Hugh  J.  White,  Washington,  D.  C. 


10 


The  School  of  Mechanical 
Engineering 

Refrigeration  Course.— Graduates  of  this  Course  will 
understand  the  principles  of  refrigeration,  the  design  and 
construction  of  refrigerating  apparatus,  and  its  installation, 
testing,  and  operation. 

Gas  Engines  Course.— This  is  intended  for  all  that  desire 
to  manufacture  and  install  gas  or  oil  engines,  and  for  all  that 
operate  or  repair  them,  or  wish  to  qualify  as  gas  engineers. 

Farm  Machinery  Course. — This  is  intended  for  traction 
engineers,  threshers,  and  farmers.  Graduates  will  thoroughly 
understand  the  principles  of  operation  of  farm  machinery 
and  be  able  to  run  traction  engines. 

The  School  of  Steam  Engineering 

Steam=Electric  Course.— This  is  a  complete  Course  on 
steam  engineering  and  electric-lighting  and  railway  work, 
and  is  intended  for  engineers,  superintendents,  etc.  of  large 
electric-lighting  or  railway  plants. 

Complete  Steam  Engineering  Course. — This  Course,  as 
its  name  implies,  is  a  complete  treatise  on  stationary  engi¬ 
neering,  and  is  intended  for  engineers,  superintendents,  etc. 
in  large  steam  plants  using  little  or  no»electric  apparatus. 

A  Chief  Engineer’s  Opinion 

I  wish  I  could  make  my  remarks 
about  the  I.  C.  S.  Steam  Engineering 
Courses  strong  enough  to  induce  every 
engineer  to  enroll.  The  knowledge 
gained  has  been  very  valuable  to  me. 

I  have  the  satisfaction  of  knowing 
not  only  the  how  but  the  why  of 
my  work.  I  now  have  charge  of  the 
Spring  Garden  Station  of  the  Phila¬ 
delphia  Water  Department,  the  largest 
plant  owned  by  the  city.  The  cost  of 
an  I.  C.  S.  Course  is  insignificant. 

Clarence  D.  Wiluason, 

1723  Norris  SL,  Philadelphia,  Pa. 

11 


The  School  of  Steam  Engineering 

Advanced  Engine  Running  Course.— This  Course  will 
qualify  engineers,  firemen,  etc.  to  take  charge  of  medium- 
sized  steam  plants. 

Engine  Running  Course.— This  Course  is  intended  for 

engineers,  firemen,  helpers,  etc.  in  small  plants,  and  to 
qualify  any  one  to  get  a  start  in  steam  engineering. 

Engine  and  Dynamo  Running. — This  is  intended  for 
those  who  wish  to  qualify  to  operate  and  care  for  the  appa¬ 
ratus  in  small  steam-electric  plants. 


The  School  of  Marine  Engineering 

Marine  Engineers’  Course.— This  Course  is  intended  for 
coal  passers,  firemen,  water  tenders,  oilers,  and  other  em¬ 
ployes  of  steam  vessels.  The  graduate  will  be  qualified  to 
pass  marine  license  examination  for  any  grade  to  which  he 
is  eligible  by  law. 


The  School  of  Locomotive  Running 

Trainmen  and  Carmen’s  Scholarships. — These  three 
Scholarships  provide  trainmen  with  special  instruction  on 
air  brakes,  train  rules,  train  heating,  car  lighting,  etc. 

What  We  Do  for  Marine  Firemen 

I  had  studied  a  good  many  versions 
of  the  so-called  “Complete  Treatise  on 
the  Steam  Engine,’’  but  I  had  never 
found  what  I  wanted  to  know  until  I 
enrolled  in  the  Schools.  Ten  times 
what  I  have  paid  for  my  Scholarship 
would  not  buy  my  Course  from  me. 
I  have  risen  from  the  position  of  fire¬ 
man  to  that  of  chief  engineer  of  an 
ocean-going  steamer.  Every  promise 
you  made  has  been  faithfully  kept, 
and  you  have  even  done  more  for  me 
than  I  expected. 

Sherman  Mallery,  Norfolk,  Va. 
12 


The  School  of  Locomotive  Running 

Locomotive  Running  Scholarships. — These  six  Scholar¬ 
ships  are  very  popular  with  locomotive  firemen  and  engi¬ 
neers.  They  furnish  instruction  in  the  construction  and 
management  of  the  locomotive  and  its  various  appliances 
and  fittings. 

Air  Brake  Scholarships. — These  five  Scholarships  are 
intended  for  enginemen  and  air-brake  inspectors.  They  pro¬ 
vide  complete  instruction  on  Westinghouse  and  New  York 
air  brakes. 

The  Roundhouse  Scholarships. — These  three  Scholar¬ 
ships  include  either  New  York  or  Westinghouse  air-brake 
instruction,  together  with  instruction  on  locomotive  boilers. 


The  School  of  Electrical  Engineering 

Electrical  Engineering  Course. — This  is  intended  for 
superintendents  of  electrical  establishments,  factory  artisans, 
draftsmen,  designers,  inventors,  and  all  others  that  wish  a 
thorough  knowledge  of  the  design  of  electrical  apparatus. 

Electrical  Course.— This  is  intended  for  those  that  desire 
to  qualify  for  any  electrical  position  that  does  not  require  a 
knowledge  of  mechanical  engineering. 

Electric  Railways  Course. — This  will  qualify  the  student 
to  construct  and  maintain  electric  railways  under  any  system. 


An  Electrical  Engineer’s  Experience 

I  have  always  thought  the  cost  of 
my  I.  C.  S.  Electrical  Course  trifling 
compared  with  the  benefits  received. 

The  last  Papers  of  the  Course  on  Elec¬ 
tric  Machine  Design  are  especially 
valuable.  Through  the  Schools,  I 
was  appointed  electrician  for  Moncton, 

N.  B.  For  some  time  I  have  been  in¬ 
stalling  complete  plants  of  all  kinds, 
making  the  specifications  myself. 

During  the  past  year,  I  have  had 
more  work  than  I  could  handle. 

Geo.  M.  Macdonald, 

Box  185 ,  Moncton ,  N.  B. 

13 


The  School  of  Electrical  Engineering 

Advanced  Electric  Railways  Course. — This  Course  is  a 
complete  treatise  on  steam  engineering  as  applied  to  electric- 
railway  plants,  and  is  intended  for  superintendents,  engi¬ 
neers,  etc.  in  large  electric-railway  plants. 

Advanced  Electric  Lighting  Course. — This  Course  is  a 
complete  treatise  on  steam  engineering  as  applied  to  electric- 
lighting  plants.  It  is  intended  for  superintendents,  engi¬ 
neers,  etc.  in  large  electric-lighting  plants. 

Electric  Lighting  and  Railways  Course.  —  This  is 
intended  for  dynamo  tenders,  stationary  engineers,  installa¬ 
tion  engineers,  and  all  who  work  around  electric-railway  or 
lighting  plants. 

Electric  Lighting  Course. — This  will  qualify  the  student 
to  successfully  install  and  operate  electric  arc-  and  incandes¬ 
cent-lighting  systems. 

Dynamo  Running  Course.— This  is  a  short  but  complete 
Course  on  the  operation  and  care  of  dynamos.  It  is  intended 
for  dynamo  tenders  and  for  those  who  wish  to  get  a  start  in 
electrical  work. 

Electric  Car  Running  Course.— This  Course  will  qualify 
the  student  to  direct  the  equipment  of  a  modern  electric 
car,  operate  it  safely  under  all  conditions,  and  pass  any 
motorman’s  or  car  inspector’s  examinations. 

Interior  Wiring.— This  will  qualify  the  student  to  do 
electric-light  wiring  and  bellwork. 

From  Conductor  to  Head  Barnman 

I  am  a  student  in  the  Electric  Car 
Running  Course,  and  am  pleased  to 
say  that  the  knowledge  gained  from 
my  Course  has  enabled  me  to  accept  a 
much  better  position.  When  I  en¬ 
rolled,  I  was  a  motorman  for  the 
Ogdensburg  Street  Railway  Company, 
but  after  applying  myself  to  my  Course 
for  some  time,  I  was  promoted  to  head 
barnman  for  the  above  company,  with 
a  better  salary,  and  have  also  been 
promised  another  increase. 

John  Henry  O’Neill, 

129  New  York  Avc.,  Ogdensburg ,  N.Y. 

14 


The  School  of  Electrotherapeutics 

Complete  Electrotherapeutic  Course. — Graduates  of 
this  Course  will  be  qualified  to  make  all  modern  and 
approved  applications  of  the  electric  current  in  the  diagno¬ 
sis  and  treatment  of  disease. 

Neurological  Electrotherapeutic  Course. — This  is  in¬ 
tended  for  physicians  and  medical  students  that  desire  a 
knowledge  of  the  treatment  by  electricity  of  the  diseases  of 
the  brain,  spinal  cord,  peripheral  nerves,  and  muscles. 

Gynecological  Electrotherapeutic  Course. — This  is  in¬ 
tended  for  physicians  that  wish  to  make  a  special  study  of 
the  diseases  peculiar  to  women. 

Surgical  Electrotherapeutic  Course. — This  is  intended 
for  surgeons  and  general  practitioners. 

Eye,  Ear,  Nose,  and  Throat  Electrotherapeutic  Course. 
This  is  intended  for  physicians  and  specialists. 

Dental  Electrotherapeutic  Course. — This  is  a  complete 
up-to-date  treatise  on  electricity  as  used  in  dental  operations. 

Roentgen  Rays  Course. — This  includes  instruction  in  the 
manipulation  and  care  of  all  up-to-date  apparatus  used  by 
recognized  Roentgen  ray  workers. 

Nurses’  Electrical  Course. — The  information  contained 
in  this  Course  will  increase  the  efficiency  and  earning  capac¬ 
ity  of  any  nurse,  and  will  make  her  more  valuable  to  the 
attending  physician. 

Genito=Urinary  Electrotherapeutic  Course. — This 
Course  is  especially  intended  for  the  genito-urinary  specialist. 


Prominent  Physicians  Commend  Our  Course 

International  Correspondence  Schools, 

,  Scranton,  Pa. 

Gentlemen:— After  having  completed  the  Electrothera¬ 
peutic  Course  I  can  tell  you  that  this  Course  is,  in  mv 
opinion,  a  wonderful  piece  of  work.  The  physician  folds 
everything  for  intelligently  applying  electricity,  aim  at  the 
same  time  is  not  bothered  with  superfluous  things— hypothe¬ 
sis,  opinions,  names,  etc.  I  call  them  superfluous  in  a .prac¬ 
tical  Course  which  aims  at  nothing  but  giving  t  ie  student  a 
thorough  knowledge  of  electricity  so  far  as  it  is  used  as  a 

therapeutic  and  diagnostic  agent. 

Dr.  A.  Decker,  1*25  Orchard  St.,  Chicago ,  III. 

15 


The  School  of  Telephone  and  Tele¬ 
graph  Engineering 

Telephone  Engineering  Course.— This  Course  will  qual¬ 
ify  students  to  maintain  and  manage  telephone  switchboards 
and  exchanges,  make  repairs  anywhere  in  the  system,  and 
take  general  supervision  of  a  plant. 

Telegraph  Engineering  Course.— This  is  intended  for 
telegraph  operators  in  commercial  or  railroad  business,  the 
military  or  the  signal  service.  It  gives  thorough  instruction 
in  all  branches  of  telegraphy.  Graduates  will  be  qualified  to 
fill  the  most  responsible  positions. 


The  School  of  Civil  Engineering 

Civil  Engineering  Course.— This  Course  is  intended  for 
practicing  bridge,  railroad,  municipal,  or  hydraulic  engi¬ 
neers,  surveyors,  and  engineers’  assistants  that  wish  to  review 
former  studies,  to  acquire  a  thorough  knowledge  of  other 
branches  of  the  profession  by  studying  those  special  branches 
of  engineering  in  which  they  lack  knowledge,  or  to  become 
qualified  as  consulting  engineers.  The  instruction  is  suffi¬ 
ciently  advanced  and  comprehensive  to  insure  to  the 
graduate  the  technical  training  necessary  to  the  successful 
prosecution  of  his  professional  work. 


Responsible  Position  Before  He  Finished  Study 


I  wish  here  to  say  that  before  I 
had  finished  the  instruction  in  “Bat¬ 
teries, ”  in  the  I.  C.  S.  Telephone  Engi¬ 
neering  Course,  the  Schools  helped 
me  to  obtain  the  position  I  now 
occupy,  that  of  assistant  electrician 
for  the  American  Bell  Telephone 
Company,  at  Goshen,  Ind.  The  only 
recommendations  I  carried  were  the 
Schools’  records  of  my  progress  in 
the  Course,  as  far  as  I  had  gone.  My 
technical  training  has  been  con¬ 
ducted  by  mail  entirely. 

W.  H.  Fox,  Goshen,  Ind. 


16 


The  School  of  Civil  Engineering 

Bridge  Engineering  Course.— This  is  intended  for  sur¬ 
veyors,  draftsmen,  bridge  engineers,  and  their  assistants, 
and  employes  in  bridge  works.  Graduates  will,  with  some 
experience,  be  able  to  design  and  superintend  the  construc¬ 
tion  of  modern  highway  and  railroad  bridges. 

Surveying  and  Mapping  Course.— This  is  intended  for 
rodmen,  chainmen,  engineers’  assistants,  and  all  that  wish 
to  become  surveyors.  Graduates  will  he  qualified  to  survey 
railroads,  farm  properties,  etc. 

Railroad  Engineering  Course. — Graduates  of  this  Course 
will  have  the  necessary  education  to  survey  and  map  out 
proposed  locations  for  railroads,  or  to  fill  responsible  posi¬ 
tions  in  the  work  of  construction  or  the  maintenance-of-way 
department. 

Hydraulic  Engineering  Course.— This  is  intended  for 
those  interested  in  irrigation,  water  supply,  etc.  Graduates 
will  have  the  necessary  education  to  design  and  install 
water-power  plants,  hydraulic  machinery,  and  water-supply 
and  irrigation  systems. 

Municipal  Engineering  Course. — This  is  intended  for 
municipal  engineers  and  contractors,  city  surveyors,  and 
their  assistants.  It  will  qualify  the  student  to  survey  and 
make  maps  and  estimates  of  proposed  sewerage  systems, 
street  improvements,  pavements,  etc.,  and  to  superintend 
their  construction. 

Earned  $30  as  Teacher:  Earns  $100  as  Surveyor 

When  I  enrolled  in  the  I.  C.  S.,  I 
was  teaching  school  at  $30  a  month. 

After  studying  three  months,  I  secured 
a,  position  as  draftsman  and  assistant 
surveyor  at  $70  a  month,  but  soon 
after  beginning  work  was  offered  $100 
a  month.  In  his  spare  time  a  man 
2an  gain  as  good  an  education  in  the 
international  Correspondence  Schools, 

Scranton,  Pa.,  as  at  the  best  colleges. 

[  heartily  recommend  the  Schools. 

Lloyd  G.  Smith, 

Deputy  County  Surveyor, 

Chinook,  Choteau  Co.,  Mont. 

17 


ihe  School  of  Mathematics  and 
Mechanics 

This  is  our  largest  School.  In  it  are  made  all  the  prelim¬ 
inary  examinations  and  corrections  in  mathematics  and 
mechanics  for  the  other  Schools.  The  Principal  is  assisted 
by  13  Special  Instructors  and  130  Examiners. 

While  most  of  the  mathematical  subjects  are  taught  in 
connection  with  other  Courses,  the  following  can  be  taken 
separately: 

Arithmetic  Course,  Part  1.— This  Course  includes  in¬ 
struction  from  the  simplest  definitions  of  Arithmetic  up  to 
and  including  ratio  and  proportion. 

Arithmetic,  Parts  1  and  2.— This  Course  includes  all 
the  subjects  in  Part  1,  together  with  instruction  in  the  sub¬ 
jects:  Percentage,  Interest,  Notes,  Bank  Discount,  Stocks  and 
Bonds,  Average  or  Equation  of  Payments,  Partnership,  and 
Alligation. 

Algebra  Course. — This  is  a  thorough  Course  in  Algebra, 
including  instruction  in  Quadratic  Equations,  the  Remain¬ 
der  Theorem,  the  Binomial  Formula,  Progressions,  Loga¬ 
rithms,  etc. 

Advanced  Algebra  Course.— This  Course  is  intended  for 
teachers  of  Algebra,  for  engineers,  and  for  all  others  that 
desire  thorough  instruction  in  higher  algebra. 


Kellar,  the  Greatest  Living  Magician,  Testifies 

Montour  House, 

Opposite  Court  House, 

J.  L.  Riehl,  Proprietor. 

Danville,  Pa.,  May  2. 

Dear  Sir: — In  reply  to  your  request  for  my  opinion  regard¬ 
ing  the  International'  Correspondence  Schools,  I  beg  to  say 
that  I  consider  the  system  of  Instruction  the  very  best  that 
can  be  desired,  and  judging  from  their  Course  in  Arithmetic, 
in  which  1  am  enrolled,  I  think  any  one  of  ordinary  intelli¬ 
gence  can  acquire  a  thorough  knowledge  of  mathematics 
by  carefully  reading  and  observing  the  rules  of  the  Instruc¬ 
tion  Papers.  The  system  is  so  very  simple  that  any  one  who 
can  read  may  learn.  Yours  truly, 

Harry  Kellar  (Magician). 

18 


The  School  of  Chemistry 

General  Chemistry  Course. — This  is  a  Course  in  gen¬ 
eral  and  analytical  chemistry,  and  is  intended  for  those  who 
desire  to  obtain  a  general  knowledge  of  chemistry  and  ana¬ 
lytical  methods  and  thus  prepare,  in  as  short  a  time  as 
possible,  for  general  laboratory  work.  Since  the  Course 
includes  an  exhaustive  treatment  of  organic  chemistry,  it 
enables  the  student  to  prepare  -for  responsible  positions  in 
the  manufacture  of  coal-tar  products  and  various  other 
organic  materials.  This  Course  also  prepares  the  student  for 
such  positions  as  pharmaceutical  chemist,  toxicologist,  etc. 

Chemistry  and  Chemical  Technology.  The  student 
in  this  Course  receives,  in  addition  to  a  thorough  training  in 
general  and  analytical  chemistry,  full  detailed  instruction 
in  the  most  important  branches  of  applied  chemistry. 

Separate  Courses  in  the  following  branches  of  applied 
chemistry  are  given:  Chemistry  and  Manufacture  oi  Sul¬ 
phuric  Acid;  Chemistry  and  Manufacture  of  Alkalies  and 
Hydrochloric  Acid;  Chemistry  and  Manufacture  of  Iron  and 
Steel;  Chemistry  and  Packing-House  Industries;  Chemistry 
and  Manufacture  of  Cottonseed  Oil  and  Products;  Chemistry 
and  Manufacture  of  Leather;  Chemistry  and  Manufacture  of 
Soap;  Chemistry  and  Manufacture  of  Cement;  Chemistry 
and  Manufacture  of  Paper;  Chemistry  and  Manufacture  of 
Sugar;  Chemistry,  Petroleum,  and  Manufacture  of  I  roducts, 
Chemistry  and  Manufacture  of  Gas. 


Drug  Clerk  Becomes  a  Chemist 


I  started  early  in  life  to  earn  my 
living  by  clerking,  and  my  lot  was 
cast  in  a  drug  store.  Before  I  enrolled 
in  the  Chemistry  Course,  I  made  sev¬ 
eral  attempts  to  educate  myself,  but 
with  little  success.  Thanks  to  the 
Schools,  I  have  mastered  chemistry  to 
a  degree  that  my  ambition  had  nei  ei 
pictured.  Soon  after  taking  up  mj 
Course,  I  took  charge  of  the  laboratoi  > 
at  E.  E.  Bruce  &  Co.,  wholesiile  drug¬ 
gists,  at  a  good  salary,  which  has  since 
been  increased  45  per  cent. 

H.  B.  Molyneaux,  Omaha ,  JSeo. 


19 


The  School  of  Drawing 

Mechanical  Drawing  Course.— The  student  that  com¬ 
pletes  this  Course  will  be  able  to  execute  neat  mechanical 
drawings.  We  have  met  with  remarkable  success  in  teaching 
this  subject  to  thousands  entirely  ignorant  of  drawing,  hun¬ 
dreds  of  whom  are  now  earning  good  salaries  as  draftsmen 
and  designers.  We  guarantee  to  qualify  ANY  ONE  to  make 
neat  mechanical  drawings  that  follows  our  directions. 

Architectural  Drawing  Course. — The  student  that  com¬ 
pletes  this  Course  will  be  able  to  make  general  and  detail 
drawings  of  architectural  structures,  and  will  be  thoroughly 
qualified  to  take  a  position  in  an  architect’s  office.  We 
guarantee  to  qualify  ANY  ONE  to  make  neat  architectural 
drawings  that  follows  our  directions. 

If  you  wish  to  learn  Mechanical  or  Architectural  Drawing, 
or  desire  to  become  a  mechanical  or  electrical  engineer,  or 
architect,  and  support  yourself  while  learning  either  of  these 
professions,  send  for  special  circular  entitled  “  Support 
Yourself.” 


Drawing  Outfit  Free 

Every  student  in  either  of  these  two  Courses  is  furnished 
with  the  Complete  Drawing  Outfit  No.  1,  valued  at  $13.55. 
He  is  permitted  to  retain  this  Outfit  for  use  indefinitely,  pro¬ 
vided  he  observes  the  terms  of  his  Contract  for  Scholarship. 


Dentist  to  Draftsman 

When  I  enrolled  in  the  I.  C.  S.  Me¬ 
chanical  Drawing  Course,  I  was  prac¬ 
ticing  dentistry.  After  partially  finish¬ 
ing  my  Course,  I  commenced  making 
drawings  for  the  Smith  Metallic  Pack¬ 
ing  Co.,  occasionally  receiving  as  high 
as  $15  fora  single  drawing,  and  having 
some  of  my  work  taken  in  preference 
to  that  done  by  the  Master  Mechanic 
of  a  Mexican  railway.  I  have  now 
become  Chief  Draftsman  for  the  Smith 
Metallic  Packing  Company,  Chicago. 

M.  E.  Hoag, 

861  Monadnock  Bldg.,  Chicago,  III. 

20 


The  School  of  Architecture 

Complete  Architectural  Course. — This  is  intended  for 
architects,  draftsmen,  contractors  and  builders,  carpenters, 
masons,  bricklayers,  building  tradesmen,  and  all  others 
desirous  of  qualifying  themselves  to  design  and  construct 
buildings.  Graduates  will  he  able  to  design,  prepare  working 
drawings  and  specifications  for  building  operations,  calculate 
quantities,  estimate  costs,  and  will  have  a  thorough  knowl¬ 
edge  of  iron  and  steel  construction. 

Architectural  Drawing  and  Designing  Course.— This  is 
intended  for  carpenters,  contractors,  architectural  draftsmen, 
and  all  that  wish  to  learn  architectural  drawing,  history,  and 
design. 

Building  Contractors’  Course.— This  will  qualify  car¬ 
penters,  masons,  bricklayers,  and  other  building  tradesmen 
to  make  and  read  plans,  estimate  accurately,  and  undertake 
general  contracting  and  building.  This  is  a  practical  Course 
in  building  construction,  containing  practical  instruction 
for  practical  men. 

Architectural  Drawing  Course. — This  Course  is  de¬ 
scribed  under  “  The  School  of  Drawing.”  See  previous  page. 
Students  in  this  Course  have  been  so  successful  that  we  will 
forfeit  $100  to  any  student  of  our  Architectural  Drawing 
Course  that  will  study  as  we  direct,  whom  we  cannot  qualify 
to  make  neat  architectural  drawings. 


From  Telegraph  Operator 

When  I  began  studying  in  the  Com¬ 
plete  Architectural  Course  of  the  In¬ 
ternational  Correspondence  Schools, 
of  Scranton,  Pa.,  I  was  a  telegraph 
operator  and  knew  nothing  whn  fever 
of  drawing,  or  of  the  profession  that  I 
am  now  following.  I  have  given  up 
my  partnership  at  Fainnount  and  am 
now  well  established  here,  with  good 
prospects  for  a  very  successful  busi¬ 
ness.  My  income  at  present  is  three 
times  what  I  was  receiving  when  I 
enrolled.  _  ,,  ...  . . 

John  C.  Tibbetts,  Grafton,  W.  Va, 

21 


to  Architect 

t  . 


The  School  of  Design 

Ornamental  Design  Course. — This  provides  instruction 
in  freehand  drawing,  sketching  from  nature,  and  conven¬ 
tionalizing  of  natural  forms  as  a  basis  for  decorative  design, 
history  of  ornament,  details  of  color,  and  construction  of  all 
typical  elements,  composition,  pencil,  pen,  wash-drawing 
and  water-color  work,  and  the  application  of  design  to  china, 
wall  paper,  lace,  book  covers,  embroidery,  furniture,  stained 
glass,  interior  decoration,  rugs,  carpets,  oilcloths,  etc.  The 
instruction  is  carefully  graded  from  the  simplest  instru¬ 
mental  work  to  the  more  complicated  water-color  rendering 
of  practical  designs. 

Drawing,  Sketching,  and  Perspective  Course. — This 

is  intended  for  teachers  that  wish  to  qualify  for  the  position 
of  drawing  inspector;  also,  for  all  that  desire  a  thorough 
knowledge  of  freehand  and  perspective  drawing.  Even  if 
the  Course  is  taken  only  for  developing  artistic  tastes  and 
perceptions,  it  is  invaluable. 


The  School  of  Sheet-Metal  Work 

Sheet=MetaI  Pattern  Drafting  Course. — This  Course  is 
intended  for  tinsmiths,  cornice  makers,  architectural  sheet- 
iron  workers,  coppersmiths,  plumbers,  etc.  Graduates  will 
be  able  to  develop  all  kinds  of  sheet-metal  patterns. 

Doubled  His  Salary  Since  Enrolling 

Before  I  enrolled  in  the  I.  C.  S.,  my 
education  consisted  of  but  four  terms 
in  a  country  district  school.  I  took 
up  the  Sanitary  Plumbing,  Heating, 
and  Ventilation  Course  and  the 
Sheet-Metal  Pattern  Draft¬ 
ing1  Course,  and  have  received 
great  benefits  from  my  instruction. 
When  I  enrolled,  my  salary  was  $9 
a  week.  I  am  now  foreman  of  a  large 
shop  doing  plumbing,  heating,  venti¬ 
lating,  and  cornice  work. 

B.  M.  Richards, 

Box  W5,  Everett ,  Wash. 


22 


The  School  of  Plumbing,  Heating, 
and  Ventilation 

Sanitary  Plumbing,  Heating,  and  Ventilation  Course. 

This  affords  an  education  in  plumbing,  heating,  and  ven¬ 
tilation  that  will  qualify  any  plumber,  steam  titter,  or  gas- 
fitter  to  fill  the  highest  positions  in  his  line  of  work.  It  is  of 
particular  value  to  such  men  as  aspire  to  become  master 
plumbers,  general  contractors,  or  heating  engineers. 

Sanitary  Plumbing  and  Gas=Fitting  Course.— This 
Course  enables  plumbers,  gas-fitters,  and  apprentices  to  do 
their  work  easier,  better,  and  more  economically,  and  to  pass 
examinations  for  license. 

Heating  and  Ventilation  Course.— This  is  intended  for 
steam  fitters,  plumbers,  and  heating  and  ventilating  engi¬ 
neers.  It  will  qualify  the  student  to  install  any  system  of 
heating  or  ventilation. 

Sanitary  Plumbing  Course.— This  is  intended  for 
plumbers  and  plumbing  apprentices  that  do  not  care  to  study 
gas-fitting  or  heating  and  ventilation.  It  will  qualify  the 
student  to  pass  any  examination  required  of  plumbers. 

Gas-Fitting  Course.— This  will  qualify  the  student  to 
calculate  illumination  required,  test  systems,  put  up  combi¬ 
nation  fixtures,  or  make  drawings  of  proposed  installations. 


From  Journeyman  to  Master  Plumber  and 

Gas-Fitter 

I  am  under  many  obligations  to  the 
I.  C.  S.  I  have  recently  passed  an 
examination  and  obtained  a  first-class 
Master  Plumber’s  license.  It  has  been 
of  inestimable  benefit  to  me.  I  most 
heartilv  recommend  the  Schools,  espe¬ 
cially  to  plumbers  who  are  desirous  of 
gaining  an  insight  to  the  technical 
theories  of  the  trade,  which  equips 
them  to  earn  larger  wages  and  the 
best  positions  as  workmen. 

Michael  L.  Sylvia, 

Plumber  and  Gas-Fitter , 

Hew  Bedford ,  Mass. 

23 


The  School  of  Mines 

Full  Mining  Course.— This  is  intended  for  mine  super¬ 
intendents,  foremen,  mining  engineers,  and  others  that  wish 
a  thorough  education  in  all  branches  of  coal  and  metal 
mining.  It  fits  the  student  to  superintend  either  coal  or 
metal  mines,  or  to  pass  mine  foreman’s  or  State  Mine  Inspect¬ 
or’s  examinations. 

Complete  Coal  Mining  Course.— This  is  intended  for 
mining  engineers,  mine  officials,  and  miners  that  wish  a  com¬ 
plete  education  in  the  methods  and  machinery  used  in  coal 
mining.  It  embraces  a  study  of  every  detail  necessary  to  fit 
a  student  for  any  position  in  or  around  either  anthracite  or 
bituminous  mines,  or  pass  the  examinations  for  mine  fore¬ 
man  or  State  Mine  Inspector. 

Short  Coal  Mining  Course. — This  contains  only  the 
information  absolutely  necessary  to  qualify  persons  to  pass 
the  mine  foreman’s  examinations,  and  those  that  finish  it 
will  have  a  good  knowledge  of  the  art  of  mining. 

Metal  Mining  Course.— This  is  intended  for  mine  offi¬ 
cials,  metal  miners,  or  men  engaged  in  ore  dressing  and  mill¬ 
ing.  It  qualifies  the  student  to  take  charge  of  modern  metal 
mines  or  mining  and  milling  machinery. 

Metal  Prospectors’  Course. — This  will  qualify  the  stu¬ 
dent  to  make  assays  of  ores  and  prospect  for  gold,  silver,  and 
other  valuable  minerals. 

Salary  Increased  $500  Per  Year 

Before  I  had  finished  the  Complete 
Coal  Mining  Course,  I  obtained  a  first- 
grade  Certificate  of  Competency  as 
mine  foreman,  and  also  a  position 
where  my  salary  was  increased  $500 
per  year.  *  I  am  successfully  handling 
the  mine  in  which  I  am  employed  as 
inside  manager  and  foreman.  From 
the  information  gained  in  my  Course. 

1  can  master  the  most  complicated 
problems  in  mine  management,  and 
do  all  my  own  surveying  and  platting. 

James  Parton, 
Monongahela  City ,  Pa. 


24 


The  School  of  Metallurgy 

Complete  Metallurgy  Course. — This  Course  is  intended 
for  metallurgists,  investors,  and  others  who  desire  a  knowl¬ 
edge  of  the  metallurgy  of  gold,  silver,  copper,  lead,  and  zinc. 
It  will  give  the  student  a  broad  field  of  usefulness  and  will 
enable  him  to  direct  metallurgical  operations  of  any  kind 
whatever. 

Milling  Course. — This  provides  instruction  for  millmen, 
bosses,  and  superintendents  of  milling  operations,  and  will 
thoroughly  qualify  the  student  for  the  highest  positions  in 
this  particular  branch  of  metallurgy.  The  Course  deals  with 
the  dry  methods  of  gold  and  silver  extraction. 

Hydrometallurgical  Course.— This  Course  fully  explains 
the  wet  methods  of  treating  ores  for  gold  and  silver  extrac¬ 
tion,  and  also  includes  thorough  instruction  in  electro¬ 
metallurgy.  It  is  intended  for  helpers,  foremen,  and  super¬ 
intendents  in  hydrometallurgical  work,  electrochemists, 
electricians,  etc. 

Smelting  Course.— This  Course  deals  with  the  prelim¬ 
inary  treatment  and  the  reduction  of  ores  of  the  common 
metals  and  the  refining  of  the  crude  products.  Graduates  of 
this  Course  will  be  qualified  to  take  charge  of  all  kinds  of 
smelting  operations. 

The  School  of  Commerce 

Failed  Before;  Succeeded  With  Us 

I  had  attended  night  school  and 
had  spent  nearly  §100  on  textbooks 
without  success  before  I  heard  of  the 
I.  C.  S.  The  only  thing  I  am  sorry  for 
is  that  I  did  not  hear  of  them  sooner. 

I  had  no  trouble  in  understanding  the 
Complete  Commercial  Course  that  I 
took;  my  instructors  taught  me  every¬ 
thing  by  mail  easily,  simply,  and  accu¬ 
rately.  The  value  of  what  I  learned  is 
shown  by  the  fact  that  during  the  year 
my  salary  has  been  increased  25  per 
cent.  Ernest  Brunelli, 

Gardiner ,  N.  Mex. 

25 


The  School  of  Commerce 

Complete  Commercial  Course.— This  Course  is  intended 
for  young  men  or  women,  in  the  city  or  country,  that  wish  to 
equip  themselves  with  a  business  education.  Graduates  will 
be  able  to  keep  books  by  single  or  double  entry,  or  perform 
the  work  of  stenographer  or  correspondent.  They  will  also 
have  a  thorough  knowledge  of  modern  office  methods,  card 
systems,  etc.,  as  used  by  the  most  successful  and  up-to-date 
commercial  houses. 

Bookkeeping  and  Business  Forms  Course.— This  Course 
is  intended  for  bookkeepers,  stenographers,  etc.  that  wish  a 
business  education.  Many  professional  bookkeepers  have 
taken  this  Course  to  get  the  up-to-date  labor-saving  methods 
that  it  contains. 

Complete  Stenographic  Course.— This  Course  will  qual¬ 
ify  the  student  for  the  position  of  stenographer.  Faithful 
study  and  practice  will  enable  him  in  a  few  months  to  acquire 
the  necessary  speed,  and,  as  competent  stenographers  are 
always  in  demand,  he  can  readily  secure  a  good  position. 


The  School  of  English  Branches 

English  Branches  Courses.— These  Courses,  two  in  num¬ 
ber,  are  intended  for  those  that  lack  a  common-school  educa¬ 
tion,  or  wish  to  try  Civil-Service  Examinations. 


Success  Won  From  Defeat 

I  made  three  attempts  to  improve 
myself  at  night  school,  but  gave  up 
each  time,  as  I  was  so  backward.  So 
lip  to  1895  I  could  only  write  my  name 
and  read  a  little.  I  then  took  the 
English  Branches  Course  and  can  now 
write  and  spell  well.  While  studying, 
I  worked  84  hours  per  week,  as  in  the 
steel  business  it  is  necessary  to  work 
Sundays.  I  am  now  a  foreman,  and 
my  salary  has  been  increased  60  per 
cent.  My  ability  to  hold  the  position 
is  due  to  the  Schools. 

Michael  Sullivan,  Latrobe ,  Pa. 

26 


The  School  of  Textiles 

Complete  Cotton  Course.— This  Course  is  intended  to 
qualify  those  that  complete  it  for  the  position  of  superin¬ 
tendent,  or  purchasing  or  selling  agent,  of  a  cotton  mill.  It 
will  also  greatly  increase  the  efficiency  of  agents,  superin¬ 
tendents,  overseers,  second  and  third  hands,  mechanics, 
spinners,  loom  fixers,  weavers,  and  all  other  workers  in  a 
cotton  mill. 

Cotton  Carding  and  Spinning  Course.— This  is  intended 
for  yarn-mill  superintendents,  carders,  spinners,  section 
hands,  card  grinders,  and  all  employed  in  cotton-yarn  mills. 
It  is  also  recommended  for  cotton-machinery  erectors,  yarn 
agents,  hosiery-mill  superintendents. 

Cotton  Designing  Course.— This  Course  is  intended  for 
designers  and  assistant  designers,  agents,  superintendents, 
overseers,  and  second  hands  in  weave  rooms;  section  hands, 
loom  fixers,  weavers,  in  cotton  mills;  dry-goods  merchants, 
salesmen  in  commission  houses,  jobbers,  and  all  men  or 
women  working  in  cotton  mills,  interested  in  cotton  design¬ 
ing,  or  desirous  of  qualifying  for  any  of  the  foregoing  posi¬ 
tions. 

Cotton  Spinning  and  Warp  Preparation  Course.— This 
is  intended  for  superintendents  of  thread  mills,  boss  spin¬ 
ners,  second  and  third  hands  in  spinning  rooms,  overseers  of 
beaming,  slasher  tenders,  and  all  men  employed  in  cotton- 
yarn  mills. 

A  Shipping  Clerk’s  Advancement 

As  a  result  of  your  training  by  mail 
I  am  at  present  bookkeeper  for  the 
Randolph  Manufacturing  Co.,  at 
Franklinville,  N.  C.  When  I  enrolled 
in  your  Complete  Cotton  Course  I  was 
working  as  shipping  clerk  for  the 
same  concern,  at  a  salary  only  half 
what  I  am  now  receiving.  1  heartily 
indorse  instruction  by  mail  in  Textile 
Design,  as  conducted  by  the  I.  C.  S. 

The  lessons  are  plain  and  to  the  point, 
and  contain  only  information  that  is 
valuable. 

Hugh  Parks,  Franklinville,  N.  C. 

27 


The  School  of  Textiles 

Cotton  Warp  Preparation  and  Plain  Weaving  Course. 

This  is  intended  for  superintendents  of  weave  mills,  boss 
weavers,  fixers,  second  and  third  hands  in  weave  rooms, 
weavers,  slasher  tenders,  etc.  It  is  also  recommended  for 
those  having  a  good  knowledge  of  yarn-mill  machinery  that 
wish  to  qualify  as  general  mill  superintendents. 

Fancy  Cotton  Weaving  Course.— This  Course  is  in¬ 
tended  for  designers  and  assistant  designers,  agents,  super¬ 
intendents,  overseers,  and  second  hands  in  weave  rooms, 
section  hands,  loom  fixers,  weavers,  and  all  others  that 
desire  a  knowledge  of  warp  preparation  and  weaving  ma¬ 
chinery  for  fancy  goods. 

Cotton  Carding,  Spinning,  and  Plain  Weaving  Course. 

This  Course  is  intended  for  those  that  desire  to  qualify  for  the 
position  of  superintendent  or  overseer  in  mills  making  plain 
cotton  goods. 

Theory  of  Textile  Designing  Course.— This  is  intended 
for  those  that  have  a  good  knowledge  of  warp  preparation 
and  weaving  machinery,  but  whose  knowledge  of  the  theory 
of  designing  is  not  complete.  It  is  recommended  to  boss 
weavers,  overseers,  second  hands,  and  others  that  desire 
instruction  on  the  analysis  and  reproduction  of  fabrics,  and 
the  drafting  of  designs.  Almost  every  textile  designer  in 
the  country  is  hampered  in  his  business  by  the  lack  of  com¬ 
petent  designers. 

Worker’s  Advancement 

When  I  enrolled  in  your  Cotton 
Carding  and  Spinning  Course  I  was 
section  hand  in  the  card  room  of  Mill 
No.  3  of  the  Eagle  &  Phoenix  Mill  Co., 
of  Columbus,  Ga.  I  am  now  second 
hand  in  their  Mill  No.  1.  Your  train¬ 
ing  has  increased  my  salary  and  bet¬ 
tered  my  prospects.  Correspondence 
instruction  is  the  only  means  by  which 
millmen  may  qualify  themselves  for 
promotion.  Mv  advice  to  ambitious 
young  men  is  that  they  enroll  in  the 
I.  C.  S.  and  study  in  their  spare  time. 
A.  W.  Pitts,  Phoenix  City,  Ala. 

28 


The  School  of  Textiles 

Complete  Textile  Designing  Course. — This  is  intended 
for  designers,  assistant  designers,  agents,  superintendents, 
overseers,  and  second  hands  in  weave  rooms;  and  for  section 
hands,  loom  fixers,  and  weavers  in  cotton,  woolen,  worsted, 
or  silk  mills. 

Woolen  and  Worsted  Designing  Course.— This  Course 
is  intended  for  designers  and  assistant  designers,  agents, 
superintendents,  overseers,  and  second  hands  in  weave 
rooms;  section  hands,  loom  fixers,  and  weavers  in  woolen 
and  worsted  mills;  dry -goods  merchants,  salesmen  in  com¬ 
mission  houses,  jobbers. 

Complete  Woolen  Course.— This  Course  is  intended  for 
agents,  superintendents,  overseers,  and  section  hands  in 
woolen  mills,  master  mechanics,  weavers,  loom  fixers;  in 
fact,  for  any  that  hold  a  position  in  a  woolen  mill. 

Woolen  Carding  and  Spinning  Course. — This  is  espe¬ 
cially  recommended  to  superintendents,  boss  carders,  boss 
spinners,  section  hands,  card  and  mule  erectors,  woolen- 
machinery  salesmen,  woolen-yarn  agents  and  merchants, 
and  also  for  the  superintendents  and  overseers  of  knitting 
mills  using  woolen  yarns. 

Woolen  Warp  Preparation  and  Weaving  Course. — This 
is  intended  for  all  that  desire  a  knowledge  of  the  preparing 
of  woolen  warps,  and  the  weaving  and  elementary  designing 
of  woolen  goods. 

Promoted  to  Pattern  Weaver 

When  I  enrolled  for  your  Textile 
Designing  Course  I  was  a  weaver. 

Since  then,  the  instruction  I  have 
gained  from  it,  together  with  my  prac¬ 
tical  experience,  has  enabled  me  to 
advance  to  the  position  ot  pattern 
weaver,  with  the  Springville  Manu¬ 
facturing  Company.  As  a  result  of  my 
experience,  I  am  free  to  state  that  1 
consider  your  correspondence  instruc¬ 
tion  in  the  manufacture  of  textiles  to 
be  all  that  is  claimed  for  it. 

C.  W.  Seifert, 

128  West  Main  St.,  Rockville,  Conn. 

29 


The  School  of  Pedagogy 

Teachers’  Course. — This  Course  is  intended  especially  for 
men 'and  women  that  wish  to  qualify  for  remunerative  and 
responsible  positions  in  the  teaching  profession. 

Methods  of  Teaching  Course.— This  Course  provides 
teachers  with  thorough  instruction  in  the  best  modern 
methods  of  teaching,  and  enables  them  to  qualify  for  the 
highest  salaried  positions. 

Drawing,  Sketching,  and  Perspective  Course.— This 

is  described  under  the  School  of  Design,  page  22. 

The  School  of  Lettering  and 
Sign  Painting 

Lettering  and  Sign  Painting  Course.— This  is  intended 

for  sign  painters,  window  dressers,  designers  of  lithographs, 
book  and  magazine  covers,  advertising  matter,  etc.,  wood 
and  metal  engravers,  jewelers,  stone  cutters,  wood  carvers, 
draftsmen,  stencil  makers,  retail  merchants,  clerks,  and  all 
others  that  wish  a  knowledge  of  correct  styles  of  lettering. 

Show=Card  Writing  Course. — This  is  intended  for  busi¬ 
ness  men,  clerks,  window  trimmers,  letterers,  and  all  others 
that  desire  a  knowledge  of  effective  and  artistic  show-card 
writing.  It  includes  the  only  complete  and  up-to-date 
instruction  on  the  subject  that  has  ever  been  prepared. 

Plates  Are  Unexcelled 

I  think  your  Course  is  the  most 
satisfactory  that  can  be  given.  The 
Bound  Volumes  constitute  a  refer¬ 
ence  library  that  is  the  best  to  be 
had,  and  even  if  I  did  not  go  through 
the  Course,  I  have  it  printed  so  plain¬ 
ly  that  I  could  teach  myself  without 
assistance,  and  your  lettering  Plates 
are  unexcelled:  (hey  are  the  correct 
thing.  My  positionnow  is  Sign  and 
Ticket  Writer  for  the  Robert  Simpson 
Co.,  Limited,  Department  Store,  of 
Toronto.  Sidney  Smith, 

414  Ossington  Ave.,  Toronto ,  Ont. ,  Can. 

30 


Lettering 


The  School  of  French 

French  Course.— This  is  intended  for  people  of  culture, 
civil  engineers,  business  men,  and  all  that  desire  a  conversa¬ 
tional  knowledge  of  the  French  Language.  The  Course  is 
taught  by  a  system  of  instruction  with  the  phonograph, 
designed  and  used  only  by  the  Schools. 

The  School  of  German 

German  Course. — This  is  taught  with  the  aid  of  the  pho¬ 
nograph,  and  is  intended  for  professional  and  business  men 
and  all  that  come  in  contact  with  German-speaking  people. 

The  School  of  Spanish 

Spanish  Course.— This  Course  is  intended  for  lawyers, 
physicians,  professional  and  business  men,  and  all  those 
whose  duties  bring  them  in  contact  with  the  Spanish-speak¬ 
ing  people  of  South  America,  Cuba,  Philippines,  or  Spain, 
This  Course  is  taught  with  the  aid  of  the  phonograph. 

The  School  of  Navigation 

Ocean  Navigation  Course.— This  Course  will  qualify 
seamen,  etc.  to  pass  examinations  for  master  or  mate  of 
ocean-going  vessels.  It  is  the  most  complete  Course  on  this 
subject  that  has  ev er  been  published,  and  graduates  ot  this 
Course  will  be  qualified  to  pass  any  nautical  examination  in 
the  United  States  or  foreign  countries. 

Lake  Navigation  Course.— This  Course  is  intended  par¬ 
ticularly  for  those  that  wish  to  pass  examinations  for  masters 
or  pilots  of  lake  and  coast  vessels,  and  also  tor  those  that 
wish  to  increase  their  grade  of  license.  It  is  the  first  and 
only  Course  on  this  subject  that  has  yet  appeared.  Graduates 
of  this  Course  will  be  qualified  to  pass  examinations  for 
master’s  or  pilot’s  license  for  vessels  engaged  in  lake  and 
coast  navigation. 


31 


The  School  of  Advertising 

Advertising  Course.— This  Course  is  designed  to  teach 
the  student  how  to  analyze  any  article  of  merchandise,  find 
its  selling  points,  and  write  and  lay  out  a  first-class  ad  that 
will  so  present  these  selling  points  as  to  impel  the  reader  to 
become  a  purchaser  of  the  article  advertised. 

The  Course  also  includes  instructioh  in  the  preparation  of 
miscellaneous  retail  advertising  matter;  retail  advertising 
management;  department-store  advertising;  and  the  estab¬ 
lishment  of  an  ad-writing  business  to  be  conducted  at  home 
or  in  an  office.  The  Course  is  designed  to  qualify  the  stu¬ 
dent  to  write  good  advertising  for  any  or  all  retail  lines  of 
business,  including  department  stores,  and  to  train  him  for 
later  advancement  to  the  position  of  advertising  manager. 

The  School  of  Window  Dressing 

The  Window  Dressing  Course. — This  Course  is  an 
elaborate  treatise  on  window  dressing,  store  decoration, 
etc.  in  all  its  branches.  It  embraces  practically  every  form 
of  commercial  decorative  treatment,  for  nearly  all  classes  of 
business.  The  Course  is  an  epitome  of  the  ideas  and  writings 
of  the  most  prominent  decorators  in  this  country.  This 
Course  will  not  only  advance  the  window  dresser  to  the 
front  ranks  of  his  profession,  but  will  also  qualify  any  one  to 
become  a  competent  window  dresser. 

The  School  of  Law 

Commercial  Law  Course. — This  Course  is  designed  to 

aid  persons  to  become  better  equipped  to  conduct  their  busi¬ 
ness;  through  it  an  opportunity  is  offered  them  to  attain  a 
knowledge  of  the  well-established  legal  rules  and  principles 
that  apply  to  and  govern  business  transactions. 

The  Course  will  be  found  especially  useful  by  the  fol¬ 
lowing:  Law  students,  mercantile  persons,  manufacturers, 
superintendents,  bankers,  insurance  officials,  bookkeepers, 
administrators,  justices,  conveyancers,  etc. 

32 


